The region bounded by ,

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

Problem

The region bounded by

x=0

x=e^{y}

, and

0\le y\le 1

is revolved about the vertical line

x=3

. Which of the following expressions gives the exact volume of the solid? (a)

\pi\bigl(5+e\bigr)

(b)

\pi\bigl(6e+\tfrac12e^{2}-5.5\bigr)

(c)

\pi\bigl(6e-\tfrac12e^{2}-5.5\bigr)

(d)

\pi\bigl(24-6e+\tfrac12e^{2}\bigr)