to find Upper and Lower Riemann Sum with exact accuracy
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Hi, In order to answer these questions, I faced problems with my code(matlab doesn't give any answer to code!! :O )!= questions= 1.Write a program which conclude approximate integral of the function=[ x^(x+sqrt(x))-e^sin(x)] , by calculating the 'Lower' and 'Upper' 'Riemann' Sum which should have maximum difference of e=0.0001 ? ###for visualizing the question and also my answer I wrote the formulas and rectangles in this picture=
in my code for ques1,I think line=[ r1=a+(i-1)*h ] makes abit trouble,but there is more!(matlab cannot run my ans totally :O ) tnx in advanve.
b=3.5;a=3.1;e=0.0001;
s1=0;s2=999;
% s1:lower Riemann Sum and s2:upper Riemann Sum
%for the "while" loop to start I had to first make "abs(s2-s1)" larger! do you recommend better way?
n=10;
%this 'n' is number of intervals or number of rectangles! which meets the need of accuracy
while abs(s2-s1) >e
s1=0;
s2=0;
for i=1:n
h=(b-a)/n; % I meant "dx" or dimension of intervals by "h"
r1=a+(i-1)*h; % for Lower Riem Sum intervals should be started from 'a'(the first bound) [I think 'cos of this line,code faces problem!]
r2=a+i*h; %but for Upper sum I started from 'a+h' or 'a+dx'
K1=r1^(r1+sqrt(r1))-exp(sin(r1));
K2=r2^(r2+sqrt(r2))-exp(sin(r2));
s1=s1+K1*h;
s2=s2+K2*h;
end
n=n+80; %here I'm acelerating accuracy to reach the disre of ques
end
s3=(s1+s2)/2; %it's appoximate integral of function
fprintf('for n=%g: lower riem=%g, Upper riem=%g, approx int=%g',n,s1,s2,s3 )
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