1 :\ I 



occurs by the assumption vcre" 1 - - 0, so that x * a (i - cos 0), 

 .prating by parts. We shall find 



- dO Ten" di - 2. 



Hence the numerator of x is f - - ' j a*. 



Also the denominator of x consists of three integrals wl. 



- (- - 4) a f . 



tO_l Q\ 



- _ J (|*. 

 3/ 



; .^__ i 



a 



solid of revolution be formed by revolving a 

 round the axis of y, we find for the position of the 

 a: ntrc of gr&N 



xample, let the cycloid y - ^(20* af) + a vers" 1 - , 

 revolve round the axis of y, and suppose that we require the 



