(adsbygoogle = window.adsbygoogle || []).push({}); Surface Area (help me to prove something:)

I was studying a bit about multiple integrals and found this theorem:

If we have function z=f(x,y) which is defined over the region R, surface S over the region is

[tex]S=\iint_R\sqrt{1+\left(\frac{\partial f}{\partial x}\right)^2+\left(\frac{\partial f}{\partial y}\right)^2}\,dA[/tex]

I wanted to prove this, because I doesn't seem to me to be trivial and I had to use nasty gradients and nontrivial things. I wonder if there is some easier proof out there?

You know, if we want to count arc length of curve given by function y=f(x), integral looks similar

[tex]L=\int_R\sqrt{1+\left(\frac{df}{dx}\right)^2}\,dx[/tex]

but in this case it is obvious...

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# Surface Area

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