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Math Help - Value of sin x for different intervals

  1. #1
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    Value of sin x for different intervals

    I have been asked what the average value of the sin x for the interval greater or equal to 0 and less than or equal to 2 pi. I just plugged in the two end values and since both are = 0 the answer is, of course, 0.


    Then I was asked what the average value of this is between 0 and pi

    Obviously I am doing something wrong because the answer is 2/pi!!! Please advise on how to do these correctly. Thank you very much
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  2. #2
    Lord of certain Rings
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    You are right actually!

    The average is 2/pi. Why do you think it is wrong?
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  3. #3
    Super Member wingless's Avatar
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    Average value of a function f(x) in the interval between a and b is
    \frac{\int^{b}_{a}f(x)~dx}{b-a}
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  4. #4
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    value of sin x

    So, if I have this right it goes like this:

    it would be the value of -cos x from 0 to pi divided by pi - 0

    -cos pi + -cos 0 /pi = 1+1 / pi or 2/pi Is this correct figuring? Thanks so much for helping out quickly!
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  5. #5
    Lord of certain Rings
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    Quote Originally Posted by Frostking View Post
    So, if I have this right it goes like this:

    it would be the value of -cos x from 0 to pi divided by pi - 0

    -cos pi + -cos 0 /pi = 1+1 / pi or 2/pi Is this correct figuring? Thanks so much for helping out quickly!
    Yes
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