Integrating sqrt(x^2+y^2) over Circle (x-1)^2+y^2<=1 using Polar Coordinates

[eoghan]

Hi there!
I have to calculate the integral of the function sqrt(x^2+y^2) over the circle (x-1)^2+y^2<=1

I use polar coordinates: rho goes from 0 to 2cos(theta) and theta goes from 0 to 2pi.
My result is that the integral is 0... is it right?

 

[jeffreydk]

Yea I did it and got 0 because you end up integrating $\cos(\theta)^3$ at the end, which is 0.

 

[Saladsamurai]

eohgan, if you think about what the geometric meaning of the integral is, it should be clear as to why your answer is zero.

 

[tiny-tim]

Hi there!
I have to calculate the integral of the function sqrt(x^2+y^2) over the circle (x-1)^2+y^2<=1

I use polar coordinates: rho goes from 0 to 2cos(theta) and theta goes from 0 to 2pi.
My result is that the integral is 0... is it right?

Hi eoghan!

erm … doesn't theta go from -π/2 to π/2?