Determining Volume using double integral

[cse63146]

Homework Statement

Find the volume of the solid in the first octant by the planes z = x + y + 1 and z = 5 - x - y

Homework Equations

The Attempt at a Solution

How would I set this up?

 

[Dick]

You would set it up by drawing the region in the z=0 (i.e. xy plane) and integrating z*dx*dy over that region.

 

[cse63146]

Are you sure it's not supposed to be dz dy dx? I went to my prof with this one, and the way he set it up as a series of triple integrals.

 

[Dick]

Your post title was "Determining Volume using double integral". It you want to set it up as a triple integral first then you integrate 1*dz*dx*dy over the volume. The integral of 1*dz is just z. It's the same thing. Now get started.

 

[cse63146]

http://img16.imageshack.us/img16/1340/39161133fw1.jpg

Its not to scale though; I just need to worry about the top right quadrant.

$$\int^{5}_{0}\int^{x - 5}_{0}\int^{5- x - y}_{0} dz dy dx + \int^{1}_{0}\int^{-x - 1}_{0}\int^{x + y +1}_{0} dz dy dx$$

How off am I?

 

[Dick]

Not too good I don't think. I'm not too sure what you are trying to draw, but your first step should be to figure out where the two planes intersect. Can you do that? I think that will help you picture the region.