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**Problem:**

Rewrite the indefinite integral ## \iint\limits_R\, (x+y) dx \ dy ## in terms of elliptic coordinates ##(u,v)##, where ## x=acosh(u)cos(v) ## and ## y=asinh(u)sin(v) ##.

**Attempt at a Solution:**

So would it be something like,

## \iint\limits_R\, (x+y) dx \ dy = \iint\limits_R\, [acosh(u)cos(v)+asinh(u)sin(v)] dx \ dy ##. I need to calculate ##dx## and ##dy## in terms of ##u## and ##v##, then substitute them in the integral, correct?

The only thing that comes to mind is the multivariable chain rule: ## \frac{dx}{dt} = \frac{\partial x}{\partial u} \frac{du}{dt}+\frac{\partial y}{\partial v} \frac{dv}{dt} ## or ## \frac{dy}{dt} = \frac{\partial y}{\partial u} \frac{du}{dt}+\frac{\partial y}{\partial v} \frac{dv}{dt} ##

Any help is appreciated. Thanks in advance.