Apentix/AP Calculus AB/Unit 8: Applications of Integration/Question

AP Calculus ABmediummcq1 pt

What is the area of the region enclosed by the graphs of $y=x^2$ and $y=2x+3$ ?

A.

9

B.

\frac{32}{3}

C.

-\frac{32}{3}

D.

\frac{16}{3}

Explanation

Core Concept

The curves intersect where $x^2=2x+3$ , so $x=-1$ and $x=3$ . The area is $\int_{-1}^3(2x+3-x^2)\,dx=[x^2+3x-\frac{x^3}{3}]_{-1}^3=\frac{32}{3}$ .

Correct Answer

B $\frac{32}{3}$

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