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

AP Calculus ABeasymcq1 pt

What is the average value of the function $f(x)=x^2$ on the closed interval $[0,3]$ ?

A.

3

B.

9

C.

27

D.

\frac{9}{2}

Explanation

Core Concept

The average value is $\frac{1}{3-0}\int_0^3 x^2\,dx$ . Since $\int_0^3 x^2\,dx=[\frac{x^3}{3}]_0^3=9$ , the average is $\frac{9}{3}=3$ .

Correct Answer

A $3$

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