Evaluate the iterated intergal by converting to polar coordinate?

**ZuzooVn** · May25-09, 09:22 AM

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

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

**tiny-tim** · May25-09, 11:54 AM

Originally Posted by ZuzooVn

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

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

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

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** · May25-09, 12:08 PM

Originally Posted by tiny-tim

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

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** · May25-09, 01:03 PM

Originally Posted by ZuzooVn

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