# Surface Integrals – On a hemisphere – Exercise 4089

Exercise

Calculate the integral

$$\int\int_S Pdydz + Qdxdz +Rdxdy$$

Where

$$P=x, Q=y, R=z$$

And the surface S is the outer side of the hemisphere

$$x^2+y^2+z^2=16, z\geq 0$$

$$\int\int_S \vec{F}\hat{n}ds=128\pi$$