lis CI:N 



FQ iv,]uiiv tlu> (vntiv ,.f | the quadrant of the 



;.se, we mu>t put c= and A = o. Hence 



4a 



Ex. 3. Let tlic curve be a cycloid whose equation is 



M 



y = V(2aa; - a; f ) + a vers" 1 - ; 



and suppose we require the centre of gravity of half the area 

 of the curve; then 



y 



r ,** r** J*i 



Now 



Also, when a; = 0, y = 0, and when a; = 2a, y ira\ 

 therefore /,*>*& = (TO (2a) f ) - //* V(2ax - x*) <fo : 

 and as f^X'Jftax x*) dx will be found = J?ra 8 , we have 

 f*yxdx = 27ra 8 J Tra* = J Tra*. 



Again, J ycir = yx-]x-j^ 



dx 



fore //"#& = 27ra* - /." *J$ax -x*)dx 

 = 2?ra 2 jTra* = }7ra f ; 



therefore x = = }a. 



