MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
The closed region S is bounded by y=x2 and y=4. A solid is built on S so that every cross section perpendicular to the x-axis is a rectangle whose height is three times the length of its base.
(a) Write a definite integral with respect to x that represents the volume of the solid.
(b) Write an equivalent definite integral with respect to y that represents the same volume.
(c) Compare the two integrals you wrote in parts (a) and (b). State which one is more efficient to evaluate and justify your choice without actually carrying out the integration.