A solid has as its base the semicircular region in the upper half-plane defined by with
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
A solid has as its base the semicircular region in the upper half-plane defined by x2+y2≤16 with y≥0. For each value of x in the base, a cross section taken perpendicular to the x-axis is a square whose base lies entirely within the semicircle.
(1) Part 1: (a) Describe, in terms of x, how the side length of each square is obtained from the geometry of the semicircle.
(2) Part 2: (b) Determine and justify the limits of integration that would be required to compute the volume of the solid.