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

AP Calculus ABeasymcq1 pt

What is the area of the region enclosed by the graph of $y=4-x^2$ and the $x$ -axis?

A.

\frac{16}{3}

B.

16

C.

\frac{64}{3}

D.

\frac{32}{3}

Explanation

Core Concept

The curve meets the $x$ -axis at $x=\pm2$ . The area is $\int_{-2}^2(4-x^2)\,dx=[4x-\frac{x^3}{3}]_{-2}^2=\frac{32}{3}$ .

Correct Answer

D $\frac{32}{3}$

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