Chapter 6.3, Problem 36ES

(a) Find the volume $V$ of the solid generated when the region bounded by $y=1/\left(1+x^4\right),y=0,x=1,$ and $x=b\left(b>1\right)$ is revolved about the $y\text{-axis}$ .

(b) Find $\underset{b\to +\infty }{\lim }V$ .