MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
The region R is enclosed by the curves x=y3−4y and x=y+2 for −3≤y≤3. A student wishes to compute the exact area of R by integrating with respect to y.
(a) Determine all values of y in the interval [−3,3] at which the two curves intersect.
(b) For each sub-interval of y that you identified in part (a), indicate which curve forms the right-hand boundary and which curve forms the left-hand boundary of R. Justify your answers analytically.
(c) Explain why a single definite integral in y is insufficient to find the area of R. Your explanation should reference the orientation you established in part (b).