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

AP Calculus ABeasymcq1 pt

The average value of $f(x)=\sqrt{x}$ on the interval $[0,4]$ is

A.

\frac{16}{3}

B.

\frac{4}{3}

C.

\frac{2}{3}

D.

\frac{8}{3}

Explanation

Core Concept

The integral is $\int_0^4\sqrt{x}\,dx=[\frac{2}{3}x^{3/2}]_0^4=\frac{16}{3}$ . Dividing by 4 gives $\frac{16/3}{4}=\frac{4}{3}$ .

Correct Answer

B $\frac{4}{3}$

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