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Homework Help: Integral of (x-100)(.002e^(-.002*x))

  1. Mar 28, 2010 #1
    1. The problem statement, all variables and given/known datafind the integral from 100 to infiniti for (x-100)(.002e^(-.002*x))



    2. Relevant equations



    3. The attempt at a solution.(xe^-(.002x))(e^(-.002x))-(-100e^(-.002x)) |from 100 to infiniti = -(100e^-.2)(e^-.2)+100e^(-.2)=14.84
    the answer should be 409.37. What am I missing, please?
     
  2. jcsd
  3. Mar 28, 2010 #2

    vela

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    Re: integration

    You didn't integrate it correctly. Post the details of your calculations so we can see where you went wrong.
     
  4. Mar 28, 2010 #3
    Re: integration

    (x-100)(.002e^(-.002*x))
    I first multiplied out these two and got .002xe^(-.002x) - .2e^(-.002x). Then integrating the .002xe^(-.002x) I integrated the e part first and then the x part to get -xe^(-.002x) * e^(-.002x) and then I integrated the .2e^(-.002x) and got -100e^(-.002x).
     
  5. Mar 28, 2010 #4

    vela

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    Re: integration

    The first integral you did is wrong. You need to do it by parts.
     
  6. Mar 28, 2010 #5
    Re: integration

    .002xe^(-.002x) - .2e^(-.002x). Ok. u=.002x du=dx
    v= -(1/.002)e^(-.002x) dv=e^(-.002x)
    so then, (.oo2x)(-(1/.002)e^(-.002x)- Integral of -(1/.002)e^(-.002x) dx from 100 to infiniti. (.oo2x)(-(1/.002)e^(-.002x) + (1/(.002*.002))e^(-.002x) from 100 to infiniti
    0 - .2*(-409.3654)+(204682.69)==way wrong answer...Oh my goodness this is the ultimate in frustration...
     
  7. Mar 29, 2010 #6

    vela

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    Re: integration

    Reformatted a bit to make it easier to read.
    That's wrong. Fix this and the value for the first integral should come out okay.
    This is only the value of the first integral. You still need to do the integral of 0.2 e^(-0.002x).
     
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