Question

triple integral x^2 given vertices

Answer 1

\[\int\limits \int\limits \int\limits xyz\]the solid tetrahedron with vertices (0,0,0)(1,0,0)(1,1,0)(1,0,1)

Answer 2

dV

Answer 3

what?

Answer 4

ignore the first part, just the integral

Answer 5

you want\[\int\int\int xyzdV\]over the terahedron?

Answer 6

yes

Answer 7

i drew it and i think it's bounded by x=1, y=0 but now I'm stuck

Answer 8

let me try to plot the points...

Answer 9

these circles are the points...

Answer 10

draw in the shape:I wrote the equation for each line
now we need the general region D under the solid

Answer 11

(that is a separate drawing in of D in the xy-plane in the upper-left)
same thing can be done on the z axis, so we have\[0\le y\le x\]\[0\le z\le x\]\[0\le x\le1\]which are our bounds
can you take it from here?