"Hamid Mavizi" <email@example.com> wrote in message <firstname.lastname@example.org>...
> Can somebody explain what is meant by an integral ? some examples?
An integral is a concept in calculus, usually covered in the second semester of calculus. The result is a function that represents the area under the original function. For example if we have f(x)=x, integrating f(x) gives a new function F(x)=(x^2)/2+c, where c is the constant of integration. Note that if you take the derivative of F(x), you get back our original function, f(x). So, if you were to look at f(x) between, say, x=0 and x=5, we know that the area formed under that segment of the function is the area of a triangle where the base=5-0, and the height=f(5)-f(0), or (1/2)(5)(5)=12.5 We get the same answer if we solve F(x) subject to these bounds. F(x)=(5^2/2)-(0^2/2)=12.5 (we can ignore c since it is taken care of by our bounds).
Let's move to a slightly more complicated example. Let g(x)=3x^3-4x. Integrating g(x) gives G(x)=(3/4)*x^4-2*x^2+c. Again notice that differentiating G(x) gives us back g(x).
I hope this helps somewhat...integration is not a topic that can be covered very quickly since there are so many things that need to be covered and various strategies needed for integrating different functions. Polynomials are pretty easy to integrate. There are some functions that cannot be integrated analytically like the examples I have given...those have to be approximated with numerical integration.
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