91Ó°ÊÓ

Find the volume of the described solid of revolution or state that it does not exist. The region bounded by \(f(x)=(x-1)^{-1 / 4}\) and the \(x\) -axis on the interval (1,2] is revolved about the \(x\) -axis.

Find the volume of the described solid of revolution or state that it does not exist. The region bounded by \(f(x)=\left(x^{2}-1\right)^{-1 / 4}\) and the \(x\) -axis on the interval (1,2] is revolved about the \(y\) -axis.

$$\text {Evaluate the following integrals.}$$ $$\int_{\pi / 6}^{\pi / 2} \frac{d y}{\sin y}$$

Use the approaches discussed in this section to evaluate the following integrals. $$\int_{0}^{\pi / 8} \sqrt{1-\cos 4 x} d x$$

Evaluate the following definite integrals. $$\int_{\sqrt{2}}^{2} \frac{\sqrt{x^{2}-1}}{x} d x$$

Use a computer algebra system to evaluate the following indefinite integrals. Assume that a is a positive real number. $$\int \frac{d x}{x\left(a^{2}-x^{2}\right)^{2}}$$

Use a substitution to reduce the following integrals to \(\int\) In \(u\) du. Then evaluate the resulting integral. $$\int \cos x \ln (\sin x) d x$$

Use a substitution to reduce the following integrals to \(\int\) In \(u\) du. Then evaluate the resulting integral. $$\int \sec ^{2} x \ln (\tan x+2) d x$$

Use a computer algebra system to evaluate the following indefinite integrals. Assume that a is a positive real number. $$\int\left(a^{2}-x^{2}\right)^{3 / 2} d x$$

Use the approaches discussed in this section to evaluate the following integrals. $$\int_{1}^{3} \frac{2}{x^{2}+2 x+1} d x$$