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Math Help - please derive this integral.. thanks a lot!

  1. #1
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    Exclamation please derive this integral.. thanks a lot!

    Last edited by vicky0514; August 25th 2008 at 08:25 AM.
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  2. #2
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    You should upload it on the internet then use the img tags for the URL of the image. Or you can just attach it here.
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  3. #3
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    Talking ...

    Quote Originally Posted by Chop Suey View Post
    You should upload it on the internet then use the img tags for the URL of the image. Or you can just attach it here.


    sorry!! i edited it..
    i really need your help!! thanks a lot!
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    to avoid confusion, i changed u to x
    Quote Originally Posted by vicky0514 View Post
    integral of e^(au)sin(nu)du=(((e^au)(asinnu-nconnu))/(a^2+n^2))+C
    do you mean \int e^{ax} \sin nx~dx = \frac {e^{ax} (a \sin nx - n \cos nx)}{a^2 + n^2} + C ?

    try integration by parts. let u = \sin nx and dv = e^{ax}~dx. (i hope you remember what u and dv mean)

    if you are really lazy, you can do a search for this question. it has been derived several times on this forum and many times on the internet, i'm sure, using both integration by parts and complex analysis
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  5. #5
    Moo
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    Hello,

    Substitute : \sin(x)=\frac{e^{ix}-e^{-ix}}{2i} \implies \sin(nx)=\frac{1}{2i} \cdot (e^{inx}-e^{-inx})

    \int e^{ax} \sin(nx) dx=\frac{1}{2i} \cdot \left(\int e^{ax}e^{inx} dx-\int e^{ax}e^{-inx} dx\right) =\frac{1}{2i} \cdot \left(\int e^{x(a+in)} dx-\int e^{x(a-in)} dx \right)

    Consider i as a constant.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Moo View Post
    Hello,

    Substitute : \sin(x)=\frac{e^{ix}-e^{-ix}}{2i} \implies \sin(nx)=\frac{1}{2i} \cdot (e^{inx}-e^{-inx})

    \int e^{ax} \sin(nx) dx=\frac{1}{2i} \cdot \left(\int e^{ax}e^{inx} dx-\int e^{ax}e^{-inx} dx\right) =\frac{1}{2i} \cdot \left(\int e^{x(a+in)} dx-\int e^{x(a-in)} dx \right)

    Consider i as a constant.
    I like that!

    when i said complex analysis, i was thinking of using e^{i \theta} = \cos \theta + i \sin \theta
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  7. #7
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    Actually e^{ax}\sin(nx)=\text{Im}\,e^{(a+in)x} and Euler gets in the game.
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