Hi, I'm having trouble understanding the solution to a question from my book. I think it's got something to do with the chain rule. The problem is to prove the change of variables formula for a double integral for the case f(x,y) = 1 using Green's theorem.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\int\limits_{}^{} {\int\limits_R^{} {dxdy} } = \int\limits_{}^{} {\int\limits_S^{} {\left| {\frac{{\partial \left( {x,y} \right)}}{{\partial \left( {u,v} \right)}}} \right|} } dudv[/tex]

The solution starts off by using some equation in the theory section allows for the following equality to be established.

[tex]\int\limits_{}^{} {\int\limits_R^{} {dxdy} } = A\left( R \right) = \int\limits_{\partial R}^{} {xdy} [/tex]

Then it says x = g(u,v) and [tex]dy = \frac{{\partial h}}{{\partial u}}du + \frac{{\partial h}}{{\partial v}}dv[/tex].

I don't understand how the expression for dy is arrived at. The variable y is a function of u and v. I can't see a way to use the chain rule here. Can someone please explain how the dy part is arrived at?

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# Chain rule

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