Calculus 2: Improper integrals

Given the improper integral from 1 to infinity of $\displaystyle \int_{1}^{\infty} \frac{1}{x^p} \, dx$, determine if it is convergent or divergent for different values of $p$.

Use the comparison theorem to determine whether the integral from 0 to $\pi$ of $\frac{\sin^2 x}{\sqrt{x}} \, dx$ is convergent or divergent.

Determine the convergence or divergence of the integral from 1 to infinity of $\displaystyle \int_{1}^{\infty} \frac{2 + e^{-x}}{x} \, dx$ using the comparison theorem.

If you look at the improper interval and the improper integral converges or diverges, whatever it does, the same is true of the series.