Evaluate the iterated intergal by converting to polar coordinate?

[ZuzooVn]

Main Question or Discussion Point

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

 

[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

0≤y≤1
0≤x≤2
0≤r≤2
0≤θ≤ pi/2

 

[tiny-tim]

0≤y≤1
0≤x≤2
0≤r≤2
0≤θ≤ pi/2

(have a pi: π )

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

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