# Math Help - interval convergence

1. ## interval convergence

For the values of p at which the integral converges, evaluate it.

I found the values of p in the interval to be from (-inf, 1), but I'm not sure how to calculate the integral itself. any help would be greatly appreciated!

2. For p < 1:
$\int_{0}^{1} \frac{1}{x^p} \: dx = \int_{0}^{1} x^{-p} \: dx = \left[ \frac{x^{-p+1}}{-p+1} \right]_{0}^{1} = \frac{1}{1-p}$.