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Homework Help: Need Help with Integral : undefined function integrand

  1. Jun 28, 2012 #1
    [itex]\int_0^{y-x} (y-x)^3f[x] dx[/itex]

    I really don't know what integration method that should be used to solve this. I would really appreciate anyone pointing me in the right direction, this problem is frustrating me! I tried integration by parts but it doesn't really get me anywhere.
     
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  3. Jun 28, 2012 #2

    LCKurtz

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    What does f[x] mean? No hope of working the problem without knowing.
     
  4. Jun 29, 2012 #3

    HallsofIvy

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    The whole problem makes no sense. In addition to f being undefined, you should not have the "integration variable", x, in the upper limit of integration- it makes no sense to say that x varies from 0 to x- y.
     
  5. Jun 29, 2012 #4
    OK thanks for the help. I guess the problem I have has some typos.

    I have a related question though referring to the Integral theorem under http://www.atp.ruhr-uni-bochum.de/rt1/syscontrol/node145.html

    I'm confused about the work at the integration by parts. It looks like he sets [itex]u = \int_0^t f[\tau] d\tau[/itex] and [itex]dv = e^{-st} dt[/itex], so that he ends up with [itex]du = f[t]dt[/itex]. I'm not following how to go from u to du.
     
  6. Jun 29, 2012 #5
    Let the antiderivative of [itex]f[/itex] be [itex]F[/itex].

    By the fundamental theorem of calculus,

    [tex]\int_0^t f(\tau) \; d\tau = F(t) - F(0)[/tex]

    Clearly, the derivative of this result is [itex]F'(t) = f(t)[/itex].
     
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