1. The problem statement, all variables and given/known data Generalize the integral from 0 to 1 of 1/(x^p) What conditions are necessary on P to make the improper integral converge and not diverge? I believe I have the answer but I would like to make it more formal and sound. Can someone help me with that? 2. Relevant equations None 3. The attempt at a solution Lim(b--> infinity) of ∫ 1/(x^p)dx (from 1 to b) = lim(b--> ∞) of ∫ x^(-p)dx (from 1 to b) = lim(b-->∞) of (x^(-p +1))/(-p+1) evaluated (from 1 to b) = lim(b--> ∞) of [(b^(-p + 1))/(-p+1) - (1^(-p+1))/(-p+1))] From here I would normally apply the limit to the last thing listed but it seems there are some constraints immediately needed. P ≠ 1 also x ≠ 0 how would I figure out what constraints need to be put on P for the improper integral to converge? By intuition I think I figured out the solution. I would need the [(b^(-p + 1))/(-p+1) portions numerators power to go negative so we can have it tend to 0 rather than infinity. Therefore I conclude that P>1 for the integral to converge.