AKKA. nurw.i: IXM>,I: VII..N. 



1 the area in bounded by 

 I the two curve* HPQB, 



upper curv<- 



y^r> uitiou to the lower curve; let OC-c, 



.'Ay for all the rcct- 



nilar to */, which are contained in the strip PQ<j 

 equal to xAr multiplied by the sum of the valued 



tie for each of these rectangles. Since 



,o value.- .*> (x) ^ (x), we hare 



. [<f> (x) - ^r (x) j as the result obtained by considering all 



the rectangles in the strip PQ<j have then to sum np 



the values of *Ax{^(x) + (x)} for all the stripe similar to 



'<id between M a ia, we in 



the value of /*x (6 <>) - ^r (x) } dx. Considerations of a 

 the denominator of x, and we obtain 



mm- 



,i(x)-^ 



iumcrator of y we observe that yAy Ax represents 



that |Mrtion >t" it which arises from the clement */; hence we 



n suit obtained from all the el i i the 



i-inini' the sum of all t 

 'he result by Ax. Now the sum of the values of 



h 3f*.4n#wr-f*wn. ] 



; ir sum of the values of the product for all the 

 and Ee, we obtain the numerator Ay. 1 1 



WTr 



w-t 



-e yalue of ^ my be written thu 



- J?l(*'.. - 



,/x 



meaning of the factors in the numerator is now ap- 

 parent; for l^(x)->Jr Ax ultimately represents the area 

 of the strip PQqp, and 4 \6 (x) -f + (x) ], wl ordinate 



of th point of fp t will ultimately be the ordinate 



