Chapter 6.5, Problem 1QCE

If $f$ is a smooth, nonnegative function on $\left[a,b\right]$ , then the surface area $S$ of the surface of revolution generated by revolving the portion of the curve $y=f\left(x\right)$ between $x=a$ and $x=b$ about the $x\text{-axis}$ is $\text{\_\_\_\_\_\_\_\_\_}$ .