For a solid whose base is the region bounded by the graphs of and on

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

Problem

For a solid whose base is the region bounded by the graphs of

y=0

and

y=\sin x

0\le x\le \pi

, the cross-sections perpendicular to the x-axis are rectangles. At each

x

, the rectangle’s height equals twice the square of its base width. Which of the following definite integrals represents the volume of the solid? (a)

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

(b)

\displaystyle \int_{0}^{\pi} 2(\sin x)^3\,dx

(c)

\displaystyle \int_{0}^{\pi} 2\sin x\,dx

(d)

\displaystyle \int_{0}^{\pi} (\sin x)^3\,dx