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Math Help - Improper Integrals

  1. #1
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    Improper Integrals

    http://www.webassign.net/cgi-bin/sym...%20dx%20%3D%20

    I know this improper integral converges, but now I don't know how to work it out and find the limit...

    Any help will be appreciated!
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  2. #2
    Super Member Anonymous1's Avatar
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    Have you ever heard of the gamma distribution? It can be shown that...

    \int_0^{\infty} x^a e^{-bx} dx= \frac{\Gamma (a+1)}{b^{a+1}} = \frac{a!}{b^{a+1}}

    \int_0^{\infty} x^1 e^{-5.9x} dx= \frac{\Gamma (2)}{(5.9)^{2}} = \frac{1!}{(5.9)^{2}}
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  3. #3
    Super Member Anonymous1's Avatar
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    You could also just use parts:

    \int_0^{\infty} udv = uv|_0^{\infty} - \int_0^{\infty} vdu

    set  u=x and dv= e^{-5.9x} to solve.
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  4. #4
    Super Member General's Avatar
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    Quote Originally Posted by Anonymous1 View Post
    You could also just use parts:

    \int_0^{\infty} udv = uv|_0^{\infty} - \int_0^{\infty} vdu

    set  u=x and dv= e^{-5.9x} to solve.
    You can not do that ..
    That is an improper integral, it should be evaluated in terms of limits ..
    We should solve it as an indifinite integral first ..
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  5. #5
    Super Member Anonymous1's Avatar
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    Quote Originally Posted by General View Post
    You can not do that ..
    That is an improper integral, it should be evaluated in terms of limits ..
    We should solve it as an indifinite integral first ..
    What do you mean? I was setting the bounds of integration as-per this problem...

    In any case: Use the gamma function, its easier.
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