Triple integral forming a solid region

[nysnacc]

Homework Statement

Homework Equations

Fubini's theorum

The Attempt at a Solution

I drawn the diagram with the limits (for x, y, and z)
and come up with something with 4 faces, 5 corners, 8 edges

is that something you guys got? Thanks

 

[andrewkirk]

The number of corners and edges are correct. I don't think the number of faces is.

 

[BvU]

I also come up with a different number of faces

 

[nysnacc]

I also come up with a different number of faces

Like how many as what am I doing wrong??

The x limit is 0 and z, so for z, it is between y and 1, so I put 1 as upper limit for x.

 

[nysnacc]

 

[LCKurtz]

Like how many as what am I doing wrong??The x limit is 0 and z, so for z, it is between y and 1, so I put 1 as upper limit for x.

One of the faces is part of the plane $x=z$. You don't have that in your picture.

 

[BvU]

I count five faces on your drawings too...
z = 1 is one plane, a square face
x = 0 is a triangular face
y = 0 is a triangular face, not a square face: x runs from 0 to z, not from 0 to 1.
the other two triangular faces have x=y=z as edge in common

 

[nysnacc]

so it's like a square on top with the edges pointering to a single point on bottom?

 

[andrewkirk]

so it's like a square on top with the edges pointering to a single point on bottom?

That's right - like the Great Pyramid (disregarding the references to 'top' and 'bottom'). This shape is known as a 'square pyramid'. The word 'square' is included to distinguish it from a tetrahedron or triangular pyramid. But in common language, the word 'pyramid' usually implies a square base.

 

[LCKurtz]

so it's like a square on top with the edges pointering to a single point on bottom?

Now that you have it, here's a nice picture:

Now the trick for you is to set up the six integrals. Do you see why when you do $dz$ first something is a bit more complicated?