Rotate an ellipse x 2/a 2+y 2/b 2 =1around the x axis to get an ellipsoid, let A >；; B, prove that the surface area of ellipsoid A=…

It is proved that the ellipsoid is cut into countless slices along the X axis, with a thickness of dx, and each segment is cylindrical with a radius of r=y=b( 1-x).

2/a 2) 1/2, surface area =dx*2pai*r,

The total surface area can be obtained by integration:

The integral value of A=dx*2pai*r in the range of -a to a is the expression given in the title.