MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Region U is bounded on the left by the parabola x=y2, on the right by the vertical line x=4, and between y=0 and y=3. This region is revolved about the vertical line x=6 to generate a solid.
(1) Write a single definite integral with respect to y whose value equals the volume of the solid. Clearly identify the integrand and the limits of integration, but do not evaluate the integral in this part.
(2) Evaluate the integral from part (a) to obtain an exact expression for the volume. Present your answer fully simplified and include π.
(3) State the units of the volume you found in part (b) and briefly explain how those units arise from the problem statement.