Question

Find the volume of the region between the graph of f(x,y)=25−x2−y2 and the xyplane

Answer 1

I would switch to polar coordinates

Answer 2

\[\int\limits_{-5}^{5}\int\limits_{-\sqrt{25-y^2}}^{\sqrt{25-y^2}}(25-x^2-y^2)dxdy\]
\[=\int\limits_{0}^{2\pi}\int\limits_{0}^{5}(25-r^2)r\,drd\theta\]
\[=\frac{625\pi}{2}\]