I'm trying to evaluate the double integral $\int_0^{10}\int_0^{(5/2)\sqrt{4-x^2}}4-x^2-\frac{4}{25}y^2 \; dy \; dx$
but using Cartesian coordinates requires the idea of trigonometric substitution and the limits aren't very nice either. So, my question is, how can I change this integral into another one in polar coordinates that would make the evaluation easier? I don't know if this helps, but the original problem was to find the solid bound in the first octant by $25z=100-25x^2-4y^2$. Thank you.