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Use a double integral to find the volume of the indicated solid

  1. Apr 29, 2014 #1
    1. The problem statement, all variables and given/known data
    Use a double integral to find the volume of the indicated solid.
    attachment.php?attachmentid=69225&stc=1&d=1398809837.png


    2. Relevant equations



    3. The attempt at a solution
    I cant find what I did wrong, it seems like a simple problem...
    $$\int_0^2 \int_0^x (4-y^{2})dydx=\int_0^2 4x-\frac{x^{3}}{3}dx$$
    $$=2x^2-\frac{x^{4}}{12}|_0^2=8-\frac{16}{12}=\frac{20}{3}$$
     

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  3. Apr 29, 2014 #2

    Zondrina

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    One of your limits for ##y## is wrong.
     
  4. Apr 29, 2014 #3
    I'm not seeing it, sorry.
     
  5. Apr 29, 2014 #4

    Zondrina

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    If you graph the region in the x-y plane, it should look something like this:

    http://gyazo.com/aedf21fdd2006d58eabea7d5b3324065

    Suppose you hold ##x## fixed and allow ##y## to vary. Then clearly from the above graph ##0 ≤ x ≤ 2## and ##x ≤ y ≤ 2##.

    Try letting ##y## be fixed and allowing ##x## to vary now. Do you get the same result?
     
  6. Apr 29, 2014 #5
    Ah right, I feel dumb now.

    Thank you.
     
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