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

AP Calculus ABeasymcq1 pt

Which expression gives the average value of a continuous function $f$ on the interval $[a,b]$ ?

A.

\frac{1}{b-a}\int_a^b f(x)\,dx

B.

\int_a^b f(x)\,dx

C.

\frac{f(b)-f(a)}{b-a}

D.

f(b)-f(a)

Explanation

Core Concept

The average value is the integral of $f$ over $[a,b]$ divided by the length $b-a$ of the interval.

Correct Answer

A $\frac{1}{b-a}\int_a^b f(x)\,dx$

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