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Homework Help: Volume of two regions using double integration

  1. Jul 9, 2010 #1
    1. The problem statement, all variables and given/known data
    The region enclosed by xy=1 and x=2 hence evaluate
    [tex]
    \iint x e^{-x} dydx
    [/tex]


    2. Relevant equations



    3. The attempt at a solution

    I m confused about their bounded region and i formed this integral to evaluate the volume

    [tex]

    \int_{2}^{\inf} \int_{0}^{1/x} x e^{-x} dydx
    [/tex]
    and i got the result 0.135

    Is this correct ?

    Thanks
     
  2. jcsd
  3. Jul 9, 2010 #2

    Mark44

    Staff: Mentor

    That's the approximate value. The exact value is e-2.

    The region over which integration takes place could be described more clearly, IMO. I would describe it as the region between the graph of xy = 1, the positive x-axis, and the line x = 2.
     
  4. Jul 9, 2010 #3
    Thanks :-)
     
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