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Average Value of a Function on an Interval

AP Calculus AB· difficulty 3/5

Average of cos⁡x\cos x on [0,π/2][0, \pi/2] is

  • A

    00

  • B

    12\tfrac{1}{2}

  • C

    11

  • D

    2π\tfrac{2}{\pi}

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Explanation

1π/2∫0π/2cos⁡x dx=(2/π)(1)=2/π\dfrac{1}{\pi/2}\int_0^{\pi/2}\cos x\,dx = (2/\pi)(1) = 2/\pi.

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