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Homework Help: Expression solution

  1. Sep 8, 2011 #1
    1. The problem statement, all variables and given/known data

    Using Leibniz rule and integration by parts, solve \frac{\partial}{\partial x} \int_0^y u dy.

    2. Relevant equations

    u = U(x) f' (\eta)

    \eta = \eta(x,y) = y g(x)
  2. jcsd
  3. Sep 8, 2011 #2


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    You need to enclose your tex in tex tags (without the space) [ tex]...[/tex].

    Is perchance that dy supposed to be dx? And if so, what have you tried?
  4. Sep 9, 2011 #3


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    In particular is u a function of both x and y?

    I don't see any need for "integration by parts". Leibniz' rule says
    [tex]\frac{d}{dx}\int_{\alpha(x)}^{\beta(x)} f(x,y)dy= \frac{d\beta}{dx}f(x,\beta(x))- \frac{d\alpha}{dx}f(x,\alpha(x))+ \int_{\alpha(x)}^{\beta(x)} \frac{\partial f}{\partial x}dy[/tex]

    So whether the derivative is with respect to x or y, that should be enough.
    (Unless u is some special function you didn't mention.)
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