1. ## Tetrahedron volume

find volume of the tetrahedron bounded by the coordinate planes and the plane 2x+y+z=4

how do i begin to find the limits of integration? This always seems to be the hardest part of these type of problems.

find volume of the tetrahedron bounded by the coordinate planes and the plane 2x+y+z=4

how do i begin to find the limits of integration? This always seems to be the hardest part of these type of problems.

Intersection point with the z-axis: put x=y=0 and you get the point $\displaystyle (0,0,4)$, with the y-axis put x=z=0 and get $\displaystyle (0,4,0)$ and with the x-axis we get $\displaystyle (2,0,0)$.
Now you can use elementary geometry to calculate the volume $\displaystyle \frac{(area\,\,of\,\,basis)\cdot height}{3}$ , or triple intgration: anyway, the volume is $\displaystyle \frac{16}{3}$, if I didn't make a mistake somewhere.

Tonio

3. so the limits of integration would be:

for z 0 to -8x-y+16

for y 0 to 4-2x

for z 0 to 2

I don't get the correct answer after using these limits