The function

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

Problem

The function

y=e^{-bx}

, where

b>0

, is defined on

0\le x\le 1

. When the region under the curve and above the

x

-axis is revolved about the

x

-axis, the solid has volume

\dfrac{\pi}{4}

cubic units. Which of the following values of

b

is closest to satisfying this condition? (a)

1

(b)

2

(c)

3

(d)

1.5