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]

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# Definite integral with variable limits of a multivariable function.

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