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Math Help - Quick Intergration question

  1. #1
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    Quick Intergration question

    How would i complete the following question:

    Find \int_{-1}^{2}x+2f(x)dx if \int_{-1}^{2}f(x)dx=5

    P.S
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  2. #2
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    Quote Originally Posted by Paymemoney View Post
    How would i complete the following question:

    Find \int_{-1}^{2}x+2f(x)dx if \int_{-1}^{2}f(x)dx=5

    P.S
    ...from what I understand of the above integration, you could simply separate
    \int_{-1}^{2}x+2f(x)dx = \int_{-1}^{2}xdx+2\int_{-1}^{2}f(x)dx

    of which the later is given
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  3. #3
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    \int_{-1}^{2}x+2f(x)~dx

    with

     \int_{-1}^{2}f(x)~dx=5

    take \int_{-1}^{2}x+2f(x)~dx apart into separate integrals

    \int_{-1}^{2}x+2f(x)~dx

    \int_{-1}^{2}x~dx+ 2\int_{-1}^{2}f(x)~dx

    using

    \int_{-1}^{2}f(x)~dx=5

    gives

    \int_{-1}^{2}x~dx+ 2\times 5

    Can you finish it from here?
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  4. #4
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    Quote Originally Posted by sym0110 View Post
    ...from what I understand of the above integration, you could simply separate
    \int_{-1}^{2}x+2f(x)dx = \int_{-1}^{2}xdx+\int_{-1}^{2}f(x)dx

    of which the later is given
    You mean
    \int_{-1}^{2}x+2f(x)dx = \int_{-1}^{2}xdx+2\int_{-1}^{2}f(x)dx


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  5. #5
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    why do you go 2 X 5??
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  6. #6
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    Quote Originally Posted by Paymemoney View Post
    why do you go 2 X 5??
    The second term in the answer is
    2\int_{-1}^2 f(x)dx

    and you said, in your first post, that
    \int_{-1}^2 f(x)dx= 5!
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