Chapter 14.6, Problem 37E

Surface integrals using an explicit description Evaluate the surface integral ${\displaystyle {\iint }_{S}f\left(x,y,z\right)}dS$ using an explicit representation of the surface.

37.     $f\left(x,y,z\right)=25-x^2-y^2$; S is the hemisphere centered at the origin with radius 5, for z ≥ 0.