Mathematics

Problem

A region is bounded above by the graph of a continuous, non-negative function

y=f(x)

on the interval

[a,b]

. The region is revolved about the

x

-axis to form a solid. Which of the following integrals gives the volume of the solid? a)

2\pi\displaystyle\int_{a}^{b} x\,f(x)\,dx

\displaystyle\int_{a}^{b} [f(x)]^{2}\,dx

\pi\displaystyle\int_{a}^{b} [f(x)]^{2}\,dx

2\pi\displaystyle\int_{a}^{b} [f(x)]^{2}\,dx