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Triple integrals, changing the order of integration

  1. Jan 31, 2013 #1
    1. The problem statement, all variables and given/known data

    Write out the triple integral for the volume of the solid shown in all six possible orders. Evaluate at least 2 of these integrals.


    2. Relevant equations

    I attached a picture of the figure. The front : x/2+z/5=1
    right : y/4+z/5=1

    3. The attempt at a solution

    I really need help with the possible orders and not the actual integration.
    I figured out two different orders but I'm not sure how to post them properly
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Jan 31, 2013 #2

    SammyS

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    Hello amalone. Welcome to PF !

    attachment.php?attachmentid=55246&d=1359687598.jpg

    You can simply describe the order in which you do the integrations, along with the limits of integration.

    For example:
    (From inner to outer)
    Integrate over x from x = 0 to x = 1 - 2z/5 .

    Integrate over y from y = 0 to y = 1 - 4z/5 .

    Integrate over z from z = 0 to z = 5 .​

    You could learn LaTeX and write:

    [itex]\displaystyle \int_{0}^{5} \int_{0}^{1 - 4z/5} \int_{0}^{1 - 2z/5\,} dx\,dy\,dz[/itex]
     
  4. Jan 31, 2013 #3
    Thanks!
     
  5. Jan 31, 2013 #4

    SammyS

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    How about describing the orders of integration that you've found ?
     
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