Finding bounds of a centroid problem

[Eng67]

I am having a problem finding the upper and lower (x,y) bounds for this problem.

Find the centroid of r = 1 + cos(theta) which lies in the 1st quadrant.

I come up with (2,0) and (1,0) or the axis intercept points. Is this the correct way to go about it?


m=((∫)[0]^2 ) (∫)[0]^1

 

[arildno]

It is simplest to calculate the coordinates of the centroid with the use of polar representation.
As a help, the area of the region is:
$$\int_{0}^{\frac{\pi}{2}}\int_{0}^{1+\cos\theta}rdrd\theta=\frac{1}{2}\int_{0}^{\frac{\pi}{2}}\frac{3}{2}+2\cos\theta+\frac{\cos{2\theta}}{2}{d\theta}=\frac{3\pi}{8}+1$$
And, most importantly, remember the relations:
$$x=r\cos\theta,y=r\sin\theta$$

 

[Eng67]

Thanks so much for the assistance!