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Math Help - Integrating by changing the order of integration

  1. #1
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    Integrating by changing the order of integration

    I have done the exercise but since I have an exam tomorrow it would be great if someone could check it. here goes:

     \int_{0}^{+\infty} \int_{0}^{x} xe^{\frac {-x^2}{t}} dt dx =  \int_{0}^{+\infty} \int_{t}^{\infty} xe^{\frac {-x^2}{t}} dx dt =  \int_{0}^{+\infty} \frac{1}{2} e^{-t} dt = \frac {-1}{2}
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  2. #2
    MHF Contributor Calculus26's Avatar
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    Not quite-- you did a great job switching the order of integration but made a mistake in the first integration.

    See attachment
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  3. #3
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    Yes I actually wrote the t down and then read it as a one haha well, i was really only wondering about changing the order of integration, otherwise I'm fine. thanks!
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