# Surface Integrals – On a plane – Exercise 4109

Exercise

Calculate the integral

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

Where

$$P=y-x, Q=x+y, R=y$$

And the surface S is the outer side of the plane

$$x+y+z=1, x\geq 0, y\geq 0, z\geq 0$$

$$\int\int_S \vec{F}\hat{n}ds=\frac{1}{2}$$