MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Consider the region enclosed by the curves y2=x and y=2−x. A solid is formed by revolving this region about the y-axis.
(a) Describe qualitatively how the distance from the y-axis to the boundary of the region varies as y increases from its minimum to its maximum value within the region.
(b) Two different integrals—one with respect to x and one with respect to y—could be set up to compute the volume of the solid. Choose which variable of integration leads to a single integral without splitting the region, and justify your choice in complete sentences.
(c) For the variable of integration you selected in part (b), write—but do not evaluate—the definite integral that gives the exact volume of the solid.