Chapter 5.5, Problem 45ES

In each part, use Theorems $\mathrm{5.5.2}$ and $\mathrm{5.5.8}$ to determine whether the function $f$ is integrable on the interval $\left[-1,1\right]$ .

(a) $f\left(x\right)=\cos x$

(b) $f\left(x\right)=\left\{\begin{array}{cc}x/\left|x\right|,& x\ne 0\\ 0,& x=0\end{array}\right.$

(c) $f\left(x\right)=\left\{\begin{array}{cc}1/x^2,& x\ne 0\\ 0,& x=0\end{array}\right.$

(d) $f\left(x\right)=\left\{\begin{array}{cc}\sin 1/x,& x\ne 0\\ 0,& x=0\end{array}\right.$