SOLID ui" Kl.\ 



left of th it* ofy are and xtan/9, and 



those of JB are and a cos/9. For the Dart to the ri 



in.- the limits ofy are ana \/(a' x*), and those 



ot s are .ir.-s,"* ami </. 11. no- 



f f*Mm9Jt\ 



I I xtljrdy + I 



- .* / J*e*fiJ* 



/ /' u "'', / j 



j J dxdy+j ^ j dy 



Similarly y may be expressed. 



. o treated this example as an illustration of intcgra- 

 :ither than for the mirposc of obtaining the result ii 



'. o might proc centre of gravity 



on the straight 1 h bisects the angle EOa. 



- straight line for tiu- initial line and using 

 polar co-ordinates, we have y - 0, and 



. /:/: 



rdrdO 



Solid of Bevolutum. 



:.ct a solid be generated by the revolution o: 



:'QE round the 

 and suppose 



we require t re of 



pra% portion of it 



per]>eiuliculRr to the axis 



the co-ordinates of 

 a point P in the curve be 



I y, and x + Ax the abscissa of an adjacent point Q. 



lives roi axis of x, the area PQML 



will generate .ich is ultimately equal to iry f Ax. 



Also the abscissa of its centre of gravity will be x ultimately. 









