# Homework Help: Expression solution

1. Sep 8, 2011

### Dkie

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. Sep 8, 2011

### LCKurtz

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?

3. Sep 9, 2011

### HallsofIvy

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

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

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.)