{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-16T00:12:35.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-16T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":50489,"title":"Find the area between curves (P1)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none 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width=\"62.5\" height=\"18\" style=\"width: 62.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e)          \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, b)\r\n  \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [3.5773, 6.1773, 5.5773, 11.2970]\r\n    assert(isempty(strfind(filetext, num2str(ii))), ... \r\n    'Do NOT use provided answers in your solution')\r\nend\r\n%%\r\na = 1; \r\nb = 1;\r\n\r\ny_correct = 3.5773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 3; \r\nb = 0.3; \r\n\r\ny_correct = 6.1773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = -1;\r\nb = 4;\r\n\r\ny_correct = 5.5773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = pi;\r\nb = exp(1);\r\n\r\ny_correct = 11.2970;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-19T12:36:27.000Z","updated_at":"2026-01-23T10:01:56.000Z","published_at":"2021-02-19T12:40:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArea between curves - Problem 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area between the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = x^2\\\\, \\\\mathrm{e}^{- x^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e  and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x) = a\\\\, x + b\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e over the interval [0 2] for different \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e coefficients:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                                                                                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"420\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"560\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e     \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                        plot of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=b=1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e)          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Ec+4iQZwQHN0GSffXQ9JKh9zOnz9/7733vvzyywkJCfX19TfffHNNTU1VVdXq1av79+8/f/781NTUqqqqnj173nPPPT/++OOpU6e8v/yTTz5p7Zm3b9/+wAMPvP766w8++KAQorGxccKECUOGDPnqq6/a2qQePXokJiaazeZXXnll7969zz//fLdu3Y4ePTp37lwd77vzgThBYbo9qEGvZ/vW6NEKKSkpa9eu9fxfwuzZs9955x33+Rd27NiRmpoaERHxww8/tDUh33777ZAhQ0aPHn3gwAHPnd99992AAQPS0tKueCxDcw6Ho7Cw0P3ut8PhKCgoGD58uKYPsQsHjZ6SnMO+5afbCUl/tDUSefvmm2969OjhPbOePXtWCDF37lwhxNixY9PS0pKTkwPYybZixYqGhgbPvjW3/v37X3/99W+++WYAQerQoYPnWKwOHTqMGDGirc9gBEFOTkKOPkFCTEiy026HPEpLS81mc3x8vPtmY2NjZGRkr169vv/++2Ce1uFwdOrUyel0Nj/16rRp095///1//vOfN9xwQzDfAm0SwOTkpkyfmJDkx4QkKY3ummtRk/fz9u/f73Q6x4wZE+TTHjlyxOl0CiFWr17dvn37Jp+dPHlyY2NjkN8CbeL/ldqbYH6CG0GSjg5GIt+sVqsQYtKkSUE+z88//+z+4O9//7vnVAuQRwB79tzok2Hpdped5s7UoKeRyLfRo0cfPnz4zJkznss3uFwul8vVrl3b/veovr7+N7/5jRDis88+u/3220O/UIRNwDv3RBB9Yped/JiQVGaEDl26dOn48eOjR48WQjQ2Nh45ciQuLs77YkKbNm3q1q3brFmz2vS0kZGR48ePP3jwYFFRUfMg7dmzZ+TIkWG60DiCFPDwJFr6lWGE0g0mJHUYoUNuLpcrISHh5MmT77333syZM90HeU+dOnXPnj3uBzgcjnHjxuXm5gZwkoWvv/568ODBgwcP/uqrr5p805EjR+bl5XHEtuYEMzx5tJgoJiT5ESRFGadDHjU1Nddee+1VV131xRdf3HDDDXfccYfZbHY4HJ6rOTz44IMzZ85MTk4O7Pmzs7MfeeSRDRs2LF++3HPnvHnzJk6cOHv27BBsAFQVkj4JIS4+uY8gyY8gKcGfDgndpcgjNTW1ffv2EydO3LFjxxNPPNG7d+8777xz7NixCQkJe/funT9/fpCnicvNzV22bNnVV189YsSIxsbG48ePL1myZNq0aaFaP6QScKIsu6r1+s+dbhCkcPEzQkK/HfJWWlpaVlY2duzYTp06ue/Jy8u7ePFiUlJSW49l8P0trrnmGs6tYDR+JsoIv2haR5BCjA4BqmsxUfzGyY+j7ELA/wgJfiuA8Gv+Wxaq96IQVgQpQEQI0BB+BzWBIPmrTQVy43cAAPyn4SBVVlaWlJT06tXLYrE0/2yQ10MKID///b4yRchisZSUlKi9CpXxQxD8EIQQ/BC08BPQapD27dv3wgsv3HbbbQUFBVOnTl26dGkATxJwdZqQKkIAoFGaDJLT6Vy1atV7770XHx9vt9vHjx8/derU3r17N3lYqHrTIiIEAKGlySB9/vnnUVFRA3f01QAABHlJREFU7uvrREdHjxkz5vDhw82DFFpTCq/61e2W9hNKqMX9mUbDD0HwQxBC8EOQniaDVFdX179/f8/NLl26lJaWNnlMSUlJMAd6Nh+ApN7zCgDap8kgOZ1O7z/FN5vNLpcrsKdizxsASEKTQerYsaP7UqFuLperxRNFExsA0BBNnvLruuuu+/bbbz03a2trExMTVVwPACB4mgzSsGHDhBCHDh0SQpw6dSo/P3/EiBFqLwoAEBStnlz16NGjy5cvj4+PLyoqysjImDRpktorAgAERatBAgDojCZ32QEA9IcgAQCkoMnDvq/I93lX9crHVtvt9vLycs/Nfv36de3aVdnVqclqtY4ePVrtVSiqxU027MugrKzs9OnT0dHRQ4YMUXstyvGx1dK+EnQYpJCcd1VzfG/17t27N27c2LFjR/fNrKysUaNGqbFMFWRnZ2/fvt1qtaq9EOW0tsnGfBlkZGQcPHgwMTGxtLS0c+fOOTk5np+AjvneanlfCb/oS2Nj4+DBg0+dOvXLL7/U1NQMGjTo+++/V3tRYXfFrV62bNnbb7+tzuLUU1tbu2LFisGDB48aNUrttSjE9yYb8GVQXFyckJBQW1vrvpmcnLxjxw51l6SAK261tK8Evb2H1OJ5V9VeVNhdcauLi4v79u1rt9sbGhpUWqMKMjMzo6Oj165dq/ZClON7kw34MoiKitq8eXNUVJT7Zp8+fc6e1f8JXK641dK+EvS2y86f867qj++tdjqdZ86cWbNmjd1ur6urmzFjRkZGhhrLVNrKlSvNZrP7D6gNwscmG/NlEBsbGxsb6/64oqIiNzc3LS1N3SUpwPdWy/xK0NuEFMLzrmqI76222WxJSUlbtmzJz8/Pzc21Wq3bt29XY5lK8/6ZGISPTTbsy8DNZrPNnTt30aJFAwYMUHstymlxq2V+JejtN7b5eVfbtdPbFNic762Oi4vLysqKi4sTQsTExEyYMKGgoECFVUJVRn4ZFBYWTp8+fc6cOUYYjzxa22qZXwl6C5Ixz7vqe6srKip27tzpuelwOCIiIhRdHyRg2JdBfn7+Qw89tHr16nnz5qm9FuX42GqZXwl6C5Ixz7va2lafOHGiurq6vr5+1apVZWVlQgibzXbgwIEpU8J4cXfIxsgvg8rKysWLF7/44ovjxo1raGhoaGjw3pegV61ttfyvBL3tzjKbzevXr/ecd3XdunXXXnut2osKu9a2OjMzc/LkySkpKenp6ampqQMHDiwsLFyyZIksf3MARRj5ZbBt27affvpp4cKFnnvuv//+lStXqrgkBbS21fK/EnR7ctXLly9HRkYa7W1tH1vtcrnq6+sN+DOBN14GcJPzlaDbIAEAtEWiNgIAjIwgAQCkQJAAAFIgSAAAKRAkAIAUCBIAQAoECQAgBYIEAJACQQIASIEgAQCkQJAAAFIgSAAAKRAkAIAUCBIAQAoECQAgBYIEAJACQQIASIEgAQCkQJAAAFIgSAAAKRAkAIAUCBIAQAoECQAgBYIEAJACQQIASOH/AwLTw009zNUfAAAAAElFTkSuQmCC\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":50489,"title":"Find the area between curves (P1)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 715.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 357.75px; transform-origin: 407px 357.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); 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style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 24.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 12.25px; text-align: left; transform-origin: 384px 12.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the area between the curves \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"89\" height=\"24\" style=\"width: 89px; height: 24px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e  and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"89.5\" height=\"19\" style=\"width: 89.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e over the interval [0 2] for different \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e  and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e coefficients:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 447px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 223.5px; text-align: left; transform-origin: 384px 223.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                                                                                                                                \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"560\" height=\"420\" style=\"vertical-align: baseline;width: 560px;height: 420px\" 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width=\"62.5\" height=\"18\" style=\"width: 62.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e)          \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, b)\r\n  \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [3.5773, 6.1773, 5.5773, 11.2970]\r\n    assert(isempty(strfind(filetext, num2str(ii))), ... \r\n    'Do NOT use provided answers in your solution')\r\nend\r\n%%\r\na = 1; \r\nb = 1;\r\n\r\ny_correct = 3.5773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 3; \r\nb = 0.3; \r\n\r\ny_correct = 6.1773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = -1;\r\nb = 4;\r\n\r\ny_correct = 5.5773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = pi;\r\nb = exp(1);\r\n\r\ny_correct = 11.2970;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-19T12:36:27.000Z","updated_at":"2026-01-23T10:01:56.000Z","published_at":"2021-02-19T12:40:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArea between curves - Problem 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area between the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = x^2\\\\, \\\\mathrm{e}^{- x^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e  and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x) = a\\\\, x + b\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e over the interval [0 2] for different \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e coefficients:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                                                                                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"420\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"560\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e     \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                        plot of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=b=1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e)          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