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I am having trouble integrating the function x^a. Take in consideration that we are not using any rules yet, but actually taking the passage of the limit. My question is:

int (from a to b) x^a dx why would it be inconvenient to divide the interval into equal parts? In the book it says we divide the interval as follows:

a, aq, aq^2, ..., aq^n-1, aq^n = b. (which is the geometric progression)

The answer is: (1/(a+1)(b^a+1 - a^a+1). But in the integration of x^2, we divide the interval from a to b in equal lengths of b/n. Why is this? Finally, do you think it is worth the time to do every single problem say in Courant's calculus book?

Any help would be greatly appreciated!

Thanks

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# Actual integration of a function

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