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