Let be the region bounded above by the graph of

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

Problem

Let

R

be the region bounded above by the graph of

y=\sin x

, below by the

x

-axis, and on the sides by

x=0

and

x=\pi

. A solid is generated by taking cross sections perpendicular to the

x

-axis; each cross section is a square whose base lies in

R

. (a) Give an expression for the side length of a square cross section at a value

x

in the interval

[0,\pi]

. (b) Set up, but do not evaluate, the definite integral that represents the volume of the solid.