Region S is bounded by the curves and together with the vertical lines and

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

Problem

Region S is bounded by the curves

y=x^{2}

and

y=6-x

together with the vertical lines

x=0

and

x=4

. Because the relative position of the two curves changes at

x=2

, S must be decomposed into subregions before its area is found. What is the exact area of S? (a)

\dfrac{38}{3}

(b)

20

(c)

\dfrac{16}{3}

(d)

\dfrac{22}{3}