Find the centroid of the region bounded by the given curves y= 8 sin 2x and 8 cos 2x from x=0 to x= pi/8

Question

Find the centroid of the region bounded by the given curves y= 8 sin 2x and 8 cos 2x from x=0 to x= pi/8

Answer 1

I don't have time to do all the computations, but the x value of the centroid is given by

 

x=[∫8x(cos(2x)-sin(2x))dx]/[∫8(cos(2x)-sin(2x))dx]       where the integrals are from 0 to pi/8

 

and the y value of the centroid is given by

 

y=[∫8(cos(2x)-sin(2x))(cos(2x)-sin(2x))/2 dx]/[∫8(cos(2x)-sin(2x))dx]     where the integrals are from 0 to pi/8