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Calculus 2: Improper integrals

Determine whether the integral from 2 to 3 of 2313xdx\displaystyle \int_{2}^{3} \frac{1}{\sqrt{3 - x}} \, dx is convergent or divergent and evaluate it if it is convergent.

Given the improper integral from 1 to infinity of 11xpdx\displaystyle \int_{1}^{\infty} \frac{1}{x^p} \, dx, determine if it is convergent or divergent for different values of pp.

Use the comparison theorem to determine whether the integral from 0 to π\pi of sin2xxdx\frac{\sin^2 x}{\sqrt{x}} \, dx is convergent or divergent.

Determine the convergence or divergence of the integral from 1 to infinity of 12+exxdx\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.

Consider the integral from 1 up to infinity of rac{x-2}{x^3+1}. Determine if this integral converges or diverges.

Consider the integral int e^{-x^2} \, dx.