Evaluate the iterated intergal by converting to polar coordinate?

[ZuzooVn]

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


http://www.ziddu.com/gallery/4894419/Untitled.jpg.html

[tiny-tim]

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


http://www.ziddu.com/gallery/4894419/Untitled.jpg.html

hmm … that's \int_0^2\int_0^{\sqrt{2x-x^2}}\sqrt{x^2+y^2} dxdy

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:

[ZuzooVn]

hmm … that's \int_0^2\int_0^{\sqrt{2x-x^2}}\sqrt{x^2+y^2} dxdy

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:

[tiny-tim]

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