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Math Help - Integral.

  1. #1
    Junior Member
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    Integral.

    Hello,

    Who can help me with this integral? given is \int e^{-x}sin(x)dx

    I can try it by integrations by parts thus u=sin(x) \rightarrow \ u'=cos(x) \ \ \ v'=e^{-x} \ \rightarrow \ v=-e^{-x}

    Then \int e^{-x}sin (x) = \ - sin (x) e^{-x}+\int e^{-x}cos(x)

    =-sin(x)e^{-x}-cos(x)e^{-x}-\inte^{-x}sin(x) now I can put the integral on the right to the left but then I find 0

    What do i wrong? Greets.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Bert
    Hello,

    Who can help me with this integral? given is \int e^{-x}sin(x)dx

    I can try it by integrations by parts thus u=sin(x) \rightarrow \ u'=cos(x) \ \ \ v'=e^{-x} \ \rightarrow \ v=-e^{-x}

    Then \int e^{-x}sin (x) = \ - sin (x) e^{-x}+\int e^{-x}cos(x)

    =-sin(x)e^{-x}-cos(x)e^{-x}-\inte^{-x}sin(x) now I can put the integral on the right to the left but then I find 0

    What do i wrong? Greets.
    You have:

    <br />
\int e^{-x}\sin(x)dx=-\sin(x)e^{-x}-\cos(x)e^{-x}-\int e^{-x}\sin(x) dx<br />

    So taking the last term on the right over to the left:

    <br />
2\int e^{-x}\sin(x)dx=-\sin(x)e^{-x}-\cos(x)e^{-x}<br />

    Hence:

    <br />
\int e^{-x}\sin(x)dx=-e^{-x}(\sin(x)+\cos(x))/2<br />

    RonL
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