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I have tried using polar coordinates:

first integrate from z=1 to z=10-x*x-4*y*y

The I integrate in the plane z=1, but here I need to integrate over an ellipse, how do I do this? When I wrote the expression to polar coordinates I got an expression for r that I couldnt integrate.

I have also tried integrating over the ellipse using cartesian coordinates, but I got stuck aswell, can someone pleas help?