AREAS 



195 



As an example, let the law of the curve be y = cr n , where c and n 

 are constants. 



FIG, 45- 



Now h = ca n and k = cb n 



Then area B = bk ah area A 



( ft^+J f 1 -- L-) - 

 X \ +!/ 



n+l 



n+ 



The area B can be determined independently. 

 For area B = I x dy 



1 Ccb n i 

 T I s 



^ Jca n 



This is an awkward integral to evaluate, more particularly on 

 account of the nature of the limits, and the work is rendered 

 more simple by expressing the integral in terms of x. 



