Find the volume of a given set

[carlosbgois]

Homework Statement

Evaluate the volume of the given set:

Homework Equations

$0≤x≤1, 0≤y≤1, 1≤z≤e^{x+y}$

The Attempt at a Solution

I got the 'right' answer but I think the solution is not correct. I did chance the last term given above to $0≤z≤e^{x+y}-1$, and then as usual, I evaluated $\int\int_{A}e^{x+y}-1dxdy$ and the result was correct.

But can I make that change on z? If I can, why? (I sense this is a stupid question, nevertheless I couldn't find the answer hehe)

Many thanks

 

[LCKurtz]

Homework Statement

Evaluate the volume of the given set:

Homework Equations

$0≤x≤1, 0≤y≤1, 1≤z≤e^{x+y}$

The Attempt at a Solution

I got the 'right' answer but I think the solution is not correct. I did chance the last term given above to $0≤z≤e^{x+y}-1$, and then as usual, I evaluated $\int\int_{A}e^{x+y}-1dxdy$ and the result was correct.

But can I make that change on z? If I can, why? (I sense this is a stupid question, nevertheless I couldn't find the answer hehe)

Many thanks

That setup is correct. When you do a volume by a double integral like that, the integrand is always $z_{upper}-z_{lower}$, which is what you have.