I have the following integral:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\int_0^{f(x,y)}{f' \sin(y-f')df'}[/itex]

Now suppose that f(x,y) = x*y, my question is how do I write the integral in terms of x and y only? Can I do something like this?

Since [itex]df=\frac{\partial f}{\partial x}dx+\frac{\partial f}{\partial y}dy[/itex] we can obtain:

[itex]\int_0^{x y}{x' y' \sin(y'-x' y') (\frac{\partial f'}{\partial x'}dx'+\frac{\partial f'}{\partial y'}dy'})[/itex]

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Definite integral with variable limits of a multivariable function.

**Physics Forums | Science Articles, Homework Help, Discussion**