A solid has base region in the -plane bounded above by and below by the -axis on the…

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

Problem

A solid has base region in the

xy

-plane bounded above by

y = 1 + \sin x

and below by the

x

-axis on the interval

0 \le x \le \pi

. For

0 \le x \le \pi/2

, cross sections perpendicular to the

x

-axis are squares. For

\pi/2 \le x \le \pi

, cross sections are rectangles whose heights are one-half the lengths of their bases. Compute the exact volume of the solid.