Help on calculus od Partial Differential Expression

[bdjerida]

Hi,

I'm looking to compute the following expression:

$$\int \left((\frac{\pat f(x,y)}{\pat x})^{2}+(\frac{\pat f(x,y)}{\pat y})^{2}\right)dxdy$$

any body could help me or there is well-known formula for this expression?

thanks,

 

[HallsofIvy]

That is, of course, the same as
$$\int f^2(x,y) \left(\frac{1}{x^2}+ \frac{1}{y^2}\right)dxdy$$

Other than that, how you integrate it will depend strongly on f(x,y).