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Math Help - Average Value of a function

  1. #1
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    Average Value of a function

    Can someone please explain how to find the average value of a function

    Say I have f(x)=X^2+2 on [1,4]. I think I have to to 1/b-a, but that is about all I know to do.
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  2. #2
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    1/(a-b) * integral of F , bounds a to b. It's a simple concept really. You have the total area of a region. If you make a rectangle from a to b with the same area, but one height obviously, the way to find this height is to divide the area by the width.
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  3. #3
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    Could you show me how to solve my example, because when I do it I do not get the correct answer which should be 9.
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  4. #4
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    Quote Originally Posted by gammaman View Post
    Can someone please explain how to find the average value of a function

    Say I have f(x)=X^2+2 on [1,4]. I think I have to to 1/b-a, but that is about all I know to do.
    \frac{1}{3} * \int_{1}^{4}x^2+2x=[\frac{1}{3}*(x^3/3+2x)]_{1}^{4}.

    (64/3 +8)-(1/3 +2)=(88/3)-(7/3)=81/3=27. Now divide by 3 and we get 9.
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  5. #5
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    Thank You for your help.
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  6. #6
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    I would suggest using the THANKS button which is at the bottom right corner of every post. Click it to indicate a useful post.
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