Evaluate \(\int_1^\infty \frac{1}{x^2}\,dx\), or state that it diverges.

Determine whether \(\int_1^\infty \frac{1}{x}\,dx\) converges or diverges.

Evaluate \(\int_0^1 \frac{1}{\sqrt{x}}\,dx\), or state that it diverges.

Determine whether \(\int_0^1 \frac{1}{x^2}\,dx\) converges or diverges.

Evaluate \(\int_0^\infty e^{-x}\,dx\), or state that it diverges.

Determine whether \(\int_2^\infty \frac{1}{x^3}\,dx\) converges, and find its value if it converges.

Evaluate \(\int_{-\infty}^{0} e^x\,dx\), or state that it diverges.

Determine whether \(\int_{-\infty}^{\infty}\frac{1}{1+x^2}\,dx\) converges, and find its value if it converges.

For which values of \(p\) does \(\int_1^\infty \frac{1}{x^p}\,dx\) converge?

Evaluate \(\int_0^4 \frac{1}{\sqrt{4-x}}\,dx\), or state that it diverges.