The region R in the xy plane is bounded by the graphs of y x 1 and y 1 and the lines 2 2 and x 3 If the density of R is 1 the mass of R is given by the integral 3 So m The moment of R about y axis is given by the integral 3 M The moment of R about z axis is given by the integral S 2 M da dr dx Evaluating these integrals the centroid of R is located at T y