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Average Value of a Function on an Interval

AP Calculus AB· difficulty 3/5

x avg

The average value of ff on [a,b][a,b] equals:

  • A

    f(a)+f(b)2\dfrac{f(a)+f(b)}{2}

  • B

    1b−a∫abf(x) dx\dfrac{1}{b-a}\int_a^b f(x)\,dx

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  • C

    ∫abf(x) dx\int_a^b f(x)\,dx

  • D

    f(b)−f(a)f(b) - f(a)

Explanation

Average value formula: fˉ=1b−a∫abf(x) dx\bar f = \frac{1}{b-a}\int_a^b f(x)\,dx.

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