A region in the -plane is bounded above by the graph of and below by the -axis

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

Problem

A region in the

xy

-plane is bounded above by the graph of

y = 4 - x^{2}

and below by the

x

-axis. The region is revolved about the

x

-axis to create a solid of revolution. Which of the following integrals gives the volume of the solid? (a)

\displaystyle \int_{0}^{2} \pi (4 - x^{2})^{2}\,dx

(b)

\displaystyle \int_{-2}^{2} \pi (4 - x^{2})^{2}\,dx

(c)

\displaystyle \int_{-2}^{2} \pi x^{2}\,dx

(d)

\displaystyle \int_{-2}^{2} \pi (4 - x^{2})\,dx