Chapter 6.6, Problem 303E

For the following exercises, approximate the mass of the homogeneous lamina that has the shape of given surface S. Round to four decimal places.

303. Compute ${\displaystyle {\iint }_{s}F\cdot NdS}$ , where $F\left(x,y,z\right)=xyi+zj+\left(x+y\right)k$ and N is an outward normal vector S, where S is the triangular region cut off from plane $x+y+z=1$ by the positive coordinate axes.