Homework $5\mathrm{.}4$ Triple Integrals

Score:$\frac{9}{18}$

Answered:$\frac{11}{17}$

Evaluate the triple integral $of$ the function $f(x,y,z)=-6x+8y$ over the solid tetrahedron bounded $by$ the planes $x=0,y=0,z=0,$ and $x+y+z=1.$ Answer exactly $or$ round $to3$ decimal places.

Hint: The graph $of$ the plane $x+y+z=1is$ below. Use the mouse $or$ arrow keys $to$ rotate the graph.