Deduct the area of an ellipsoid whose equation is given by $ \frac {x ^ 2} {a ^ 2} + \frac {y ^ 2} {b ^ 2} + \frac {z ^ 2} {c ^ 2} = $ 1
How to calculate this area using volume difference? Do the volume of this ellipsoid minus the ellipsoid volume of dimensions $' a = a-h, b '= b-h, c' = c-h$, with $h \implies 0$
And if not, how can I solve it? I thought about parameterizing and using Jacobin
This is a difficult problem (harder than the length of an ellipse), there is no closed-form expression in the general case. https://en.wikipedia.org/wiki/Ellipsoid#Surface_area.
The difference of volumes doesn't work because the thickness is not uniform.