Find the definite integral that correctly represents the area of the region enclosed…

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

Problem

Find the definite integral that correctly represents the area of the region enclosed by the curves

x = y^{2}

and

x = 5 - y

for

0 \le y \le 2

. (a)

\displaystyle \int_{0}^{2} \bigl[y^{2} - (5 - y)\bigr]\,dy

(b)

\displaystyle \int_{0}^{\frac{\sqrt{21}-1}{2}} \bigl[(5 - y) - y^{2}\bigr]\,dy

(c)

\displaystyle \int_{0}^{2} \bigl[(5 - y) - y^{2}\bigr]\,dy

(d)

\displaystyle \int_{0}^{5} \bigl[(5 - y) - y^{2}\bigr]\,dy