A region in the first quadrant is bounded above by the horizontal line
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
A region in the first quadrant is bounded above by the horizontal line y=2, on the right by the curve y=x, and on the left by the y–axis. The region is revolved about the horizontal line y=3 to generate a solid.
(a) Write, but do not evaluate, a definite integral that gives the volume of the solid when the calculation is carried out with respect to x. Clearly indicate the limits of integration and the expressions for the outer and inner radii.
(b) Write, but do not evaluate, a definite integral that gives the volume of the same solid when the calculation is carried out with respect to y. Clearly indicate the limits of integration and the expressions for the outer and inner radii.
(c) Describe which of the two integrals you would choose for an exact numerical evaluation. Explain your choice by comparing the complexity of the integrand and the bounds in each orientation.