Consider the region bounded by and

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

Problem

Consider the region bounded by

x=f(y)

and

x=g(y)

, where

f(y)\ge g(y)\ge0

0\le y\le b

. The region is revolved about the

y

-axis. Which integral gives the volume

V

of the resulting solid? (a)

V=\pi\displaystyle\int_{0}^{b}\bigl(f(y)-g(y)\bigr)\,dy

(b)

V=\pi\displaystyle\int_{0}^{b}\bigl[(f(y)-g(y))^{2}\bigr]\,dy

(c)

V=\pi\displaystyle\int_{0}^{b}\bigl[(f(y))^{2}-(g(y))^{2}\bigr]\,dy

(d)

V=2\pi\displaystyle\int_{0}^{b}\bigl[(f(y))^{2}-(g(y))^{2}\bigr]\,dy