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Average Value of a Function on an Interval

AP Calculus AB· difficulty 2/5

Average value of f(x)=4−x2f(x) = 4 - x^2 on [0,2][0, 2] is

  • A

    44

  • B

    83\tfrac{8}{3}

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  • C

    88

  • D

    43\tfrac{4}{3}

Explanation

12∫02(4−x2) dx=12(8−8/3)=12⋅163=8/3\dfrac{1}{2}\int_0^2 (4 - x^2)\,dx = \dfrac{1}{2}\bigl(8 - 8/3\bigr) = \dfrac{1}{2}\cdot \dfrac{16}{3} = 8/3.

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