Mathematics

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

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

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

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