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Integration help pls?

  1. Jan 26, 2010 #1
    integration help pls???

    Hi Guys

    i'm having real trouble with finding the working out of this. can anybody please help

    f(x)=∫4te^((-2t)^2) dt = 1-e^((-2t)^2)

    limits are 0 & x

    any help would be really appreciated

    it's not homework, i'm just trying to figure out something that i did a few years ago

    thanks
    daisy
     
  2. jcsd
  3. Jan 26, 2010 #2

    CompuChip

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    Re: integration help pls???

    e^((-2t)^2) is an antiderivative (up to numerical constants) of t e^((-2t)^2)
    You can check this by differentiation.

    To do it rigorously, let u = (-2t)^2 and do variable substitution
     
  4. Jan 26, 2010 #3
    Re: integration help pls???

    thanks for help

    So du=-4t dt and dv=4te dt so v=∫4te dt=4te

    Then put ie in ∫u dv=uv-∫v du?

    Sorry it really has been a while since I've done any calculus
     
  5. Jan 27, 2010 #4

    CompuChip

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    Re: integration help pls???

    You are confusing partial integration with variable substitution.

    There is no v or dv. Just replace t by u and dt by du (using u = 4 t2 and du = 4t dt), and do the integral in u. Also note that (-2t)2 = (-2)2 t2 = 4 t2, not -4t2.
     
  6. Jan 27, 2010 #5
    Re: integration help pls???

    the integral solution is 4x^2. but then you still have the right side. are you solving for t in terms of x?
     
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