Let be the region in the first quadrant that is bounded by the graph of
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Let S be the region in the first quadrant that is bounded by the graph of y=x, the x–axis, and the vertical line x=4. The region is revolved about the x–axis, generating a solid.
(a) Write a single definite integral whose value equals the volume of the solid.
(b) Evaluate the integral obtained in part (a) to find the exact volume of the solid in terms of π. Show all work leading to your result.