MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
A region R is enclosed by the graphs of y=ln(x), y=0, and x=e. The region is revolved about the horizontal line y=−2 to generate a solid.
(a) Both x-integration and y-integration are possible for finding the volume. Write one integral for the volume using x as the variable of integration and a separate integral for the volume using y as the variable of integration. Do not evaluate either integral.
(b) Compare the two integrals obtained in part (a). Identify which integral is algebraically simpler to evaluate and explain your reasoning.
(c) Evaluate the integral you identified as simpler in part (b) to obtain the exact volume of the solid.