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Double integral

  1. Dec 4, 2009 #1
    1. The problem statement, all variables and given/known data
    [tex]\int[/tex][tex]\int[/tex]D[tex]\left|x\right|[/tex]dA
    D= X2+y2<=a2 where a>0


    2. Relevant equations
    [tex]\int[/tex][tex]\stackrel{\Pi/2}{0}[/tex][tex]\int[/tex][tex]\stackrel{a}{0}[/tex] r cos [tex]\Theta[/tex] r dr d[tex]\Theta[/tex]

    I hope that's clear...

    I evaluate this to [tex]\frac{a^3}{3}[/tex] sin [tex]\Theta[/tex]


    sin [tex]\Pi[/tex]/2 = 1

    so I get [tex]\frac{a^3}{3}[/tex]

    the book says the answer is 4 [tex]\frac{a^3}{3}[/tex]



    I can't see where the 4 is coming from.

    can some one explain this to me?
     
  2. jcsd
  3. Dec 4, 2009 #2

    zcd

    User Avatar

    Your domain of [0,pi/2] only includes a quarter of the entire circle.
     
  4. Dec 4, 2009 #3
    Of course. Thanks.
     
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