The curves and intersect at and

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

The curves

x=y^2

and

x=y+2

intersect at

y=-1

and

y=2

. A student plans to compute the area of the region enclosed by the two curves by integrating with respect to

y

. Which statement accurately describes how the student should set up the integral? (a) Two integrals are required, one from

y=-1

y=0

and another from

y=0

y=2

, because the line crosses the

y

-axis and changes which curve is on the right. (b) The area should be found by integrating with respect to

x

, using two separate integrals, because the region is not bounded by a single pair of functions for all

x

. (c) A single integral from

y=-1

y=2

is sufficient because

x=y+2

remains to the right of

x=y^{2}

on the entire interval. (d) A single integral from

y=-1

y=2

should be used, but the integrand must be

(y^{2})-(y+2)

since the parabola is to the right of the line throughout the interval.