Two adjacent rectangles rest on the -axis

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Two adjacent rectangles rest on the

x

-axis. Rectangle

A

spans

0\le x\le1

and has height

2

. Rectangle

B

spans

1\le x\le2

and has height

3

. Both rectangles are revolved together about the

x

-axis. Determine the exact volume of the resulting solid.