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Math Help - integration by parts - e^-x

  1. #1
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    integration by parts - e^-x

    how does the first underlined part become the second..

    does the.. x e^x-1 cancel? where does the -2 come from?

    Help. Thankss
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  2. #2
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    Nothing cancels, it's from filling in the boundaries.

    \left[-(x^2+1)e^{-x}\right]^{1}_{0}=\left(-(1^2+1)e^{-1}\right)-\left(-(0^2+1)e^{0}\right) = -2e^{-1}+1
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  3. #3
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    Quote Originally Posted by calculus0 View Post
    how does the first underlined part become the second..

    does the.. x e^x-1 cancel? where does the -2 come from?

    Help. Thankss
    Dear calculus0,

    \left[-(x^{2}+1)e^{-x}\right]_{0}^{1}=\left[-(1^{2}+1)e^{-1}\right]-\left[-(0^{2}+1)e^{-0}\right]=-2e^{-1}+1

    Hope this will help you.
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  4. #4
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    thank you both.
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