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Thread: 2 integration by parts problems

  1. #1
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    2 integration by parts problems

    1)$\displaystyle \int_{0}^{\frac{\pi }{2}}x^2 cos2x dx$
    2)$\displaystyle \int_{0 }^{\pi }e^x sin2x dx$

    work iv done so far.
    1)$\displaystyle uv-\int v du$
    $\displaystyle \frac{x}{2}sin 2x -\int x sin 2x dx$
    2)$\displaystyle uv-\int v du$
    $\displaystyle sin 2x e^x-\int e^x \frac{1}{2} cos 2x dx$

    am i doing these right? I think i am doing them wrong can anyone help?
    thanks for the help in advance
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by dandaman View Post
    1)$\displaystyle \int_{0}^{\frac{\pi }{2}}x^2 cos2x dx$
    2)$\displaystyle \int_{0 }^{\pi }e^x sin2x dx$

    work iv done so far.
    1)$\displaystyle uv-\int v du$
    $\displaystyle \frac{x^{{\color{red}2}}}{2}sin 2x -\int x sin 2x dx$
    2)$\displaystyle uv-\int v du$
    $\displaystyle sin 2x e^x-\int e^x \frac{1}{2} cos 2x dx$

    am i doing these right? I think i am doing them wrong can anyone help?
    thanks for the help in advance
    You're doing them right (except note the correction in red)! Now apply integration by parts to $\displaystyle \int x\sin\left(2x\right)\,dx$ and $\displaystyle e^x\cos\left(2x\right)\,dx$
    Last edited by Chris L T521; Aug 31st 2009 at 07:47 PM.
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  3. #3
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    I think for number 1 he lost an x.
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  4. #4
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    k thanks for the response I got -pi/4 for #1
    but for #2, i cant get the answer.
    this is what i get and can't continue from here.

    $\displaystyle \int e^xsin2xdx=sin 2x e^x - \frac{1}{2} cos 2x e^x +\frac{1}{4}\int e^xsin2x dx$
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  5. #5
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    You actually can continue. For example consider the following:
    $\displaystyle
    y = 5x^2 + 3y$
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  6. #6
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    Quote Originally Posted by dandaman View Post
    k thanks for the response I got -pi/4 for #1
    but for #2, i cant get the answer.
    this is what i get and can't continue from here.

    $\displaystyle \int e^xsin2xdx=sin 2x e^x - \frac{1}{2} cos 2x e^x +\frac{1}{4}\int e^xsin2x dx$
    That is A= B- C+ (1/4)A. Can you solve that for A?
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