Double integral

  • Thread starter yoleven
  • Start date
  • #1
78
0

Homework Statement


[tex]\int[/tex][tex]\int[/tex]D[tex]\left|x\right|[/tex]dA
D= X2+y2<=a2 where a>0


Homework 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?
 

Answers and Replies

  • #2
zcd
200
0
Your domain of [0,pi/2] only includes a quarter of the entire circle.
 
  • #3
78
0
Of course. Thanks.
 

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