Consider the region in the -plane bounded above by the curve

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

Problem

Consider the region in the

xy

-plane bounded above by the curve

y = \sin x + 1

, below by the

x

-axis, and between

x = 0

and

x = \pi

. The region is revolved about the line

y = -1

to form a solid. What is the volume of this solid? (a)

\dfrac{9\pi^{2}}{2} + 8\pi

(b)

\dfrac{7\pi^{2}}{2} + 8\pi

(c)

3\pi^{2} + 8\pi

(d)

\dfrac{3\pi^{2}}{2} + 4\pi