Triple Integrals: Find Volume of Region Bounded by x+y, 10, 0, 0

[mirandasatterley]

Homework Statement

Find the volume of the region bounded by z=x+y, z=10, and the planes x=0, y=0

The Attempt at a Solution

If I want to integrate with respect to z,y, then x;
Then I think the limits of integration would be 0≤x≤z-y, so for x the be its largest, set y=0 and z to be large = 10, therefore, 0≤x≤10

for y, keep x constant;
0≤y≤z-x, for y to be large, z should be large, therefore 0≤y≤10-x

and z is already given by the equations in the question; 10≤z≤x+y

I'm not sure that these are right because I have a hard time picturing it in 3D??
Also, Since no function was given, am i just integrating 1, or is a function supposed to be made from the equations in the question?

 

[tiny-tim]

Find the volume of the region bounded by z=x+y, z=10, and the planes x=0, y=0
…
If I want to integrate with respect to z,y, then x …

Hi mirandasatterley!

No, integrating three times is not usually a sensible way to do it.

To find a volume, divide into slices, find the area of each slice, and just integrate once.

In this case, use horizontal slices (z = constant), of thickness dz, and integrate the area.

I'm not sure that these are right because I have a hard time picturing it in 3D??

The horizontal slices will be triangles.

Also, Since no function was given, am i just integrating 1, or is a function supposed to be made from the equations in the question?

Yes.