I am confused by this prospect. We have a semicircle with radius r whose centroid is given by 4r/3pi. Can we obtain the area of the semi circle by integrating from the centroid of the semi circle.
I saw that we could integrate from the centre of the full circle by evaluating integral through a sector like this ![Area of a sector](http://community.wolfram.com//c/portal/getImageAttachment?filename=WolframAlpha--integral__0_5___r_2__from_theta_0_to_theta_theta__Definite_integral____2017_10_31_22_31.png&userId=1211375)
But how could we do it from the centroid of the semi circle?