25G NEW MODE OF REPRESENTING 



we should only have to integrate Y^dx, between 

 the limits .r = and x = 2. 



"2 /'2 /*2 



.-. I X,da;=\ dx-\ (^ - ^Y dx 

 'o Jo 1 "> •'^ • 



'1 r2 



= 2 - \ {\ - x) dx -\ {\ - x)dx 

 .1 



1 1 



=2-1+2-1+2 



= 1, the required area. 



These forms of definite integrals can, by proper 

 substitutions, be reduced to uniform limits. 



The above example has been taken from a 

 memoir on the Inverse method of Definite In- 

 tegrals, communicated to the Cambridge Philoso- 

 phical Society, by the late Rev. Robert Murphy, 

 B.A. It is impossible to mention this great 

 mathematician's name without feelings of deep 

 regret, that he was cut off from his investigations 

 at such an early period of his life. In looking 

 over the long list of distinguished names that the 

 University of Cambridge has produced since the 



