In the first quadrant

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

Problem

In the first quadrant, region

S

is enclosed by

y = \cos x

y = \sin x

, and the

y

-axis. The region is revolved about the line

y = -1

. Which of the following definite integrals represents the volume of the solid generated? (a)

V = \pi \displaystyle\int_{0}^{\pi/4}\bigl[(\sin x+1)^2-(\cos x+1)^2\bigr]\,dx

(b)

V = \pi \displaystyle\int_{0}^{\pi/4}\bigl[\cos ^2x-\sin ^2x\bigr]\,dx

(c)

V = \pi \displaystyle\int_{0}^{\pi/4}\bigl[(\cos x+1)^2-(\sin x+1)^2\bigr]\,dx

(d)

V = \pi \displaystyle\int_{0}^{\pi/2}\bigl[(\cos x+1)^2-(\sin x+1)^2\bigr]\,dx