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Math Help - integrals

  1. #1
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    integrals

    f(x,t)= t^3/ x^2 * exp(-t^2/x) if x>0

    0 if x=o

    F(t)= integral from 0 to 1 f(x,t) dx

    Show that dF/dt is not equal to integral from 0 to 1 df/dt dx
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  2. #2
    Senior Member
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    Quote Originally Posted by Smiling View Post
    f(x,t)= t^3/ x^2 * exp(-t^2/x) if x>0

    0 if x=o

    F(t)= integral from 0 to 1 f(x,t) dx

    Show that dF/dt is not equal to integral from 0 to 1 df/dt dx
     F(t) = \int^1_0 \frac{t^3}{x^2}*exp(-t^2/x) dx


    = [t*exp^(- t^2/x)]_x=0^{x=1} = t*exp^(- t^2)


    F(t) = t*exp^(- t^2)

    -----

    dF/dt = exp(- t^2)*(1-2t^2)


    df/dt = \frac{t^2*exp^(- t^2/x)*(3x - 2*t^2)}{x^3} =: g


    \int^1_0 g dx = exp(- t^2)*(1 - 2*t^2)


    Is there any chance you mean f(x,t) = \frac{t^3}{x^2*exp(-t^2/x)}?
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