Mathematics

Mathematics

Problem

Consider the region bounded by

x=f(y)

and

x=g(y)

, where

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

on

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

Browse the problem library