Multiple Integral question

1. Jul 27, 2008

It has been a long while since I've done any multiple integral stuff and I must say this question posed to me has me stumped, even though I suspect it is trivial.

1. Find the volume of the of the region bounded by the first octant and x+z=3 and y+5z=15

I figure since it is in the first octant of 3D Euclidean coordinate system the lower bound should involve at some point x,y,z = 0, and I think I also need to get the point of intersection of the two planes, which I came up with as y = 5x which I have no idea if it is helpful or not. So some guidance would be appreciated if possible!

2. Jul 27, 2008

rootX

Get the plane equation, and you would see that you are finding volume under that plane.

http://img77.imageshack.us/img77/1989/96274221xa5.png [Broken]

Last edited by a moderator: May 3, 2017
3. Jul 28, 2008

HallsofIvy

Staff Emeritus
The plane rootX is talking about is the one containing the lines x+ z= 3 with y=0, y+ 5z= 15 with x= 0, and 5x+ y= 15 with z= 0.