A region is bounded above by the graph of a continuous

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

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

(b)

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

(c)

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

(d)

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