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Mathematics LibreTexts

5.4E: Average Value of a Function Exercises

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    13817
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    5.4: The Average Value of a Function Exercises

    In the following exercises, find the average value \(\displaystyle f_{ave}\) of f between a and b, and find a point c, where \(\displaystyle f(c)=f_{ave}\)

    110) \(\displaystyle f(x)=x^2,a=−1,b=1\)

    111) \(\displaystyle f(x)=x^5,a=−1,b=1\)

    Answer:
    \(\displaystyle f_{ave}=0\)

    112) \(\displaystyle f(x)=\sqrt{4−x^2},a=0,b=2\)

    113) \(\displaystyle f(x)=(3−|x|),a=−3,b=3\)

    Answer:
    \(\displaystyle \frac{3}{2}\) 

    114) \(\displaystyle f(x)=sinx,a=0,b=2π\)

    115) \(\displaystyle f(x)=cosx,a=0,b=2π\)

    Answer:
    \(\displaystyle f_{ave}=0\)

    J5.4.1) \(\displaystyle f(x)=\sqrt[3]{x},a=1,b=8\)

    Answer:
    \(\displaystyle f_{ave}= \frac{45}{28}\)

    J5.4.2) \(\displaystyle f(x)=\frac{1}{x},a=2,b=5\)

    Answer:
    \(\displaystyle f_{ave}= \frac{1}{3}ln(2.5)\)