Evaluate the iterated intergal by converting to polar coordinate?

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tiny-tim
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Help me Evaluate the iterated intergal by converting to polar coordinate:


http://www.ziddu.com/gallery/4894419/Untitled.jpg.html
hmm … that's [tex]\int_0^2\int_0^{\sqrt{2x-x^2}}\sqrt{x^2+y^2} dxdy[/tex]

ok … I assume you know how to convert dxdy into r and θ

and for the limits, convert y2 ≤ 2x - x2 into r and θ also :wink:
 
  • #3
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hmm … that's [tex]\int_0^2\int_0^{\sqrt{2x-x^2}}\sqrt{x^2+y^2} dxdy[/tex]

ok … I assume you know how to convert dxdy into r and θ

and for the limits, convert y2 ≤ 2x - x2 into r and θ also :wink:
0≤y≤1
0≤x≤2
0≤r≤2
0≤θ≤ pi/2
:smile:
 
  • #4
tiny-tim
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0≤y≤1
0≤x≤2
0≤r≤2
0≤θ≤ pi/2
:smile:
(have a pi: π :wink:)

No, the upper limit of r will depend on θ.

I repeat … convert y2 ≤ 2x - x2 into r and θ
 

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