Chapter 6.5, Problem 23ES

Assume that $y=f\left(x\right)$ is a smooth curve on the interval $\left[a,b\right]$ and assume that $f\left(x\right)\ge 0$ for $a\le x\le b$ . Derive a formula for the surface area generated when the curve $y=f\left(x\right),a\le x\le b,$ is revolved about the line $y=-k\left(k\ge 0\right)$ .