Consider the region enclosed by the parabola and the line .

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

Problem

Consider the region

S

enclosed by the parabola

y^{2}=4x

and the line

y=2x-4

. (a) Rewrite each curve in the form

x=f(y)

. (b) Find the exact

y

-coordinates of all points where the two curves intersect. (c) Set up—but do not evaluate—a single definite integral with respect to

y

whose value equals the area of

S

. Clearly indicate the integrand and the limits of integration. (d) Evaluate the integral from part (c) to obtain the exact area of

S