Question

Set up a double integral in rectangular coordinates for calculating the volume of the solid under the graph of the function f(x,y) = 32 - x^2 - y^2 and above the plane z = 7.

(include limits of integration)

Answer 1

I am not sure in rectangular coordinates\[z = 32 - x^{2} - y^{2}\]\[7 = 32 - x^{2} - y^{2}\]\[x^{2} + y ^{2} = 25\]\[-5\le x \le5\]\[-\sqrt{25 - x^{2}} \le y \le \sqrt{25 - x^{2}}\]\[\int\limits\limits_{-5}^{5}\int\limits\limits_{-\sqrt{25 - x ^{2}}}^{\sqrt{25 - x^{2}}}\left( 32-x^{2}-y^{2} \right)dydx\]