Consider the region in the first quadrant bounded on the left by
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Consider the region S in the first quadrant bounded on the left by x=y2, on the right by x=y+2, and below by the y-axis. A solid has base S. For each real number y in the domain of S, the cross section taken perpendicular to the y-axis is a semicircle whose diameter lies in the base region.
Answer the following.
(a) Express the diameter of a typical semicircular cross section as a function of y. Justify your expression.
(b) Evaluate the volume of the solid. Present your setup and complete calculation.