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Tongji Advanced Mathematics, 6th Edition, Volume II, 160. Ellipsoid first calculates a double integral. It's hard to calculate. How did you come straight out of the book?
Double integral does not need to be calculated by integral.

Because the integrand function is 1, the double integral is equal to the area of Dz, that is.

The area of an ellipse (note that it is not an ellipsoid) can be directly calculated by the area formula of the ellipse.

This problem is to calculate a double integral first, which is as simple as that.

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