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Multivariable Calculus

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Surface Area Element of Explicit Equation

MVCALC-L0DFYK

Find the surface area element $dS$ for the graph of:

$$z=f(x,y)=e^{2xy}-y$$

A

$dS=\sqrt{4(x^2+y^2)e^{4xy}-4xe^{2xy}+2} dxdy$

B

$dS=\sqrt{(x^2+y^2)e^{4xy}-4xe^{2xy}+1}dxdy$

C

$dS=\sqrt{4y^2e^{4xy}-4xe^{2xy}+1}dxdy$

D

$dS=\sqrt{(x^2+y^2)e^{4xy}-4ye^{2xy}+2}dxdy$

E

$dS=\sqrt{4x^2e^{4xy}-4xe^{2xy}+1}dxdy$