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Math Help - Finding a definite integral from other given definite integrals.

  1. #1
    Junior Member bijosn's Avatar
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    Finding a definite integral from other given definite integrals.

    What is this technique called?:

    Suppose f is continuous and \displaystyle \int_{-2}^{2}f(x)dx = 4 and
    \displaystyle \int_{-2}^{5}g(x)dx = 2

    Determine \displaystyle \int_{5}^{2}f(y)dy



    I am just doing this out of memory, tell me if its right
    \displaystyle \int_{5}^{2}f(y)dy = -(\int_{-2}^{5}g(x)dx) - (-(\int_{-2}^{2}f(x)dx))
    \displaystyle \int_{5}^{2}f(y)dy = - 2 - (-4) = 2
    Last edited by mr fantastic; April 11th 2011 at 10:10 AM. Reason: Re-titled, copied title into main body of post.
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  2. #2
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    I don't think it would have a name. It isn't that significant.
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  3. #3
    Junior Member bijosn's Avatar
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    no name? is my calculation atleast correct?
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  4. #4
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    Quote Originally Posted by bijosn View Post
    no name? is my calculation atleast correct?
    Assuming it's meant to be f and not g in the second given integral, your answer is correct. (If it was wrong the TheCoffeeMachine would have said so in his/her post, by the way).
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  5. #5
    Junior Member bijosn's Avatar
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    thank you, I apologize for not being sufficiently intuitive to understand the subtle ways of the coffee machine
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