Mathematics

Problem

A solid has base the region enclosed by the curves

y=8-x^{2}

and

y=x^{2}

. At every value of

x

, the cross section perpendicular to the

x

-axis is a rectangle of height

5

. Which of the following integrals equals the volume of the solid? a)

\displaystyle \int_{-2}^{2} 5\,(8-x^{2})\,dx

\displaystyle 2\int_{-2}^{2} 5\,(8-2x^{2})\,dx

\displaystyle \int_{-2}^{2} 5\,(8-2x^{2})\,dx

\displaystyle \int_{-2}^{2} (8-2x^{2})\,dx