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The surface is defined by , the top half of the ellipsoid , so the surface-area element is
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Iterating in the order results in the integral
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≐ 0.0003283936762
where , the equation of the ellipse, has been solved for , and .
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As a function of , the integrand is sufficiently complicated that Maple cannot find an antiderivative for it. Hence, the iterated integral is evaluated numerically.
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