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I'm trying to find

[tex] \iint_S \sqrt{1-\left(\frac{x}{a}\right)^2 -\left(\frac{y}{b}\right)^2} dS [/tex]

where S is the surface of an ellipse with boundary given by [itex]\left(\frac{x}{a}\right)^2+\left(\frac{y}{b}\right)^2 = 1 [/itex].

Any suggestions are appreciated!

Thanks,

Nick