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Double integrals

  1. May 6, 2009 #1
    1. The problem statement, all variables and given/known data

    integrate y DA over the regions s, where s is in the first quadrant bounded by x = y^2 and x = 8 - y^2

    2. Relevant equations



    3. The attempt at a solution

    If the y wasnt there i would evaluate two integrals and subtract them to get the area.
    But since the y is there, can i still evaluate them seperatly with the y in place and subtract.
     
  2. jcsd
  3. May 6, 2009 #2

    tiny-tim

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    Hi joemama69! :smile:
    and which axis??
    (not sure what you're subtracting, but:) yes … what's worrying you about that? :smile:
     
  4. May 8, 2009 #3
    ya i was thinkin to hard

    heres what i did, i broke it into two intigrals and added them

    first intigral

    i differentiated y dy from 0 to x^(1/2)
    then i did in trems of x from 0 to 4 and got an area for 4

    2nd integral

    i differentiated y dy from 0 to (8-x)^(1/2)
    then i did in trems of x from 4 to 8 and got an area for 4

    4 + 4 = 8 is that right
     
  5. May 9, 2009 #4

    tiny-tim

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    Yup, that's fine! :biggrin:

    (though you could have saved a little work by pointing out that the region was obviously symmetric about x = 4, so all you had to do was evaluate one integral, and then double it. :wink:)
     
  6. May 9, 2009 #5
    ya i noticed that, but i figured for my teachers sake i should do it thoroughly
     
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