1 ifl ;i:i: UF C.IIAVITV 



few 



and * V2a - *) A -* + |/(a - *)* db 



therefore * </(2a -*)<& = (2a) ; 



f* IT 27ra(2a)* 8 , .1 

 thus J yx*dx= - i;> -M*. 



Also I Wf*db- 2?ra (2a) 4 - \ (2a) f , (see page 1 



; f <* 



therefore 



4-7T _ 32 2a / S\ 



T 45 3 r i.-J 



Ex. 5. Suppose the cycloid 



/M 



J(2ax x") + a vers" 1 



to revolve round the axis of y, and that we require the centre 

 of gravity of the surface generated by that half of the curve 

 for which y is positive. 



. 



-. 



J.VO* /> 



Tlie value of the numerator was found in the preceding 

 example; and 



