Let be the region bounded by the curves and .

MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Let

R

be the region bounded by the curves

x=3y

and

x=y^{2}+2

. (a) Solve for all

y

-values at which the curves intersect. (b) Write, but do not evaluate, a definite integral whose value equals the area of

R

. (c) Evaluate the integral obtained in part (b) to determine the exact area of

R