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Math Help - integration by parts - please help!

  1. #1
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    integration by parts - please help!

    Hi,
    I am trying to integrate (x^5)/7680 . exp (-x/2) dx between 0 and 1. I've had various attempts at this and this is what i have done so far....
    Taken the 1/7680 outside the integration
    Using integation by parts I have assigned u=x^5 and dv/dx = exp(-x/2). when i integrate exp(-x/2) i get v = -2exp(-x/2), and du/dx = 5x^4 - is this correct?
    This integration results in....
    -2x^5exp(-x/2) - the integral of -8x^4 . exp(-x/2)
    which also has a product so i do a series of integration of parts to nock down the power each time to get the solution in terms of a x^5 + x^4 +x^3 etc....
    But i mut be doing something wrong as the answer is 1.4x10^-5 and i get 0.189!
    I would really appreciate some help on this integration as I've spent so long trying to figure it out and this is my last resort!
    Thanks
    zxcv784
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  2. #2
    Moo
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    Hello,

    Quote Originally Posted by zxcv784 View Post
    Hi,
    I am trying to integrate (x^5)/7680 . exp (-x/2) dx between 0 and 1. I've had various attempts at this and this is what i have done so far....
    Taken the 1/7680 outside the integration
    Using integation by parts I have assigned u=x^5 and dv/dx = exp(-x/2). when i integrate exp(-x/2) i get v = -2exp(-x/2), and du/dx = 5x^4 - is this correct?
    This integration results in....
    -2x^5exp(-x/2) - the integral of -8x^4 . exp(-x/2)
    which also has a product so i do a series of integration of parts to nock down the power each time to get the solution in terms of a x^5 + x^4 +x^3 etc....
    But i mut be doing something wrong as the answer is 1.4x10^-5 and i get 0.189!
    I would really appreciate some help on this integration as I've spent so long trying to figure it out and this is my last resort!
    Thanks
    zxcv784
    Your method is the one you have to use, but there's a mistake (in red, it should be -2*5=-10), does it change the end or was that just a typo ?
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  3. #3
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    thanks for your quick reply!

    that was a stupid mistake, thanks for spotting it! I have gone through the integration again

    after the first integration stage i now get...

    -2x^5.exp(-x/2) -integral of -10x^4 . exp(-x/2)

    after continuing the integrations my final result is:

    -2x^5.exp(-x/2) - 20x^4.exp(-x/2) + 160x^3.exp(-x/2) - 960x^2.exp(-x/2) + 3840x.exp(-x/2) - 7680exp(-x/2)

    I have tried to substitue the boundaries into this (x=1 and x=0) and then divide by 7680 but get a minus number so i must have gone wrong somewhere, any ideas?

    your help on this is greatly appreciated.

    zxcv784
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  4. #4
    Moo
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    Hm, when dealing with integration by parts, you have the term :

    [-2x^5 e^{-x/2}]_0^1

    This is equal to -2(1)^5 e^{-1/2}-\underbrace{(-2(0)^5 e^{-0/2})}_{=0}=-2 e^{-1/2}

    Do it from the beginning, and be careful with the signs ~

    Can you just show your work ? (or steps)
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