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Find the volume of a given set

  1. May 1, 2012 #1
    1. The problem statement, all variables and given/known data
    Evaluate the volume of the given set:


    2. Relevant equations
    [itex]0≤x≤1, 0≤y≤1, 1≤z≤e^{x+y}[/itex]


    3. 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 [itex]0≤z≤e^{x+y}-1[/itex], and then as usual, I evaluated [itex]\int\int_{A}e^{x+y}-1dxdy[/itex] 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
     
  2. jcsd
  3. May 1, 2012 #2

    LCKurtz

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    Science Advisor
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    Gold Member

    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.
     
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