For , a solid has cross sections perpendicular to the -axis that are semicircles…

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

Problem

For

0\le x\le L

, a solid has cross sections perpendicular to the

x

-axis that are semicircles whose diameters are given by

3x+1

. If the volume of the solid is

\dfrac{19\pi}{4}

cubic units, what is the value of

L

? (a)

3

(b)

2

(c)

\dfrac{3}{2}

(d)

4