Consider the region in the first quadrant bounded on the right by the curve
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Consider the region in the first quadrant bounded on the right by the curve x=y1, bounded on the left by the y-axis, and bounded above and below by y=3 and y=1, respectively. This region is revolved about the y–axis.
(1) Part 1: (a) Identify the appropriate geometric model (disk or washer) for the cross-sections obtained by slicing perpendicular to the y–axis. Justify your choice.
(2) Part 2: (b) Write a single definite integral whose value equals the volume of the solid generated. Express all quantities as functions of y.
(3) Part 3: (c) Evaluate the integral found in part (b) to obtain the exact volume.