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Math Help - Average value of a function

  1. #1
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    Average value of a function

    What is the basic process of finding the average value for this problem. Find the average value of the function f(x)= sin(x) on the interval [0, pi]
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  2. #2
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    You basically solve that integral, and multiply it by 1/(upper bound-lower bound); in this case, it would be 1/Pi.
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  3. #3
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    So I'd integrate that function, then multiply by 1/ 1/pi, but where'd you get 1/pi from?
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  4. #4
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    Just one over pi. Because that's the definition of average value: 1/(b-a). So you have endpoints 0 and Pi, then the term b-a becomes Pi.
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    Ahh, I see now. Thank you!!
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  6. #6
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    Quote Originally Posted by Hibijibi View Post
    What is the basic process of finding the average value for this problem. Find the average value of the function f(x)= sin(x) on the interval [0, pi]
    Average value of f(x) on [a,b] is \frac{1}{b-a}\int_a^{b}f(x)dx

    Therefore for f(x)=\sin(x) and [0,\pi] youd have average value is

    \frac{1}{\pi-0}\int_0^{\pi}\sin(x)dx=\frac{1}{\pi}\bigg[-\cos(x)\bigg]\bigg|_0^{\pi}=\frac{2}{\pi}
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  7. #7
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    Ahh, I will def need to remember that for tomorrows exam. Thank you!
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