The region enclosed by the graphs of and on the interval is revolved about the -axis
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
The region enclosed by the graphs of y=x2 and y=4−x2 on the interval −2≤x≤2 is revolved about the x-axis, forming a solid.
(a) Find all x-values in [−2,2] at which the two curves intersect.
(b) On each subinterval determined by the intersection points, state which curve lies farther from the x-axis and which lies closer. Justify your answer analytically.
(c) Write a set of definite integral expressions (one for each subinterval, if necessary) whose sum equals the exact volume of the solid.
(d) Evaluate the integral(s) to determine the exact volume of the solid.