MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Consider the curves C1 and C2 defined by
C1:x=y3−3y and C2:x=y.
The two curves intersect at three distinct y–values and enclose a single finite region.
(a) Find all y–coordinates where C1 and C2 intersect. List them in increasing order.
(b) On each subinterval determined by the intersection ordinates in part (a), identify which curve forms the right‐hand boundary of the enclosed region. Justify your answer analytically.
(c) Compute the exact area of the region enclosed by the two curves. Be sure to account for any change in orientation identified in part (b).