218 A. Mukhopadhyay — Elliptic Functions and Mean Values. [Fo. 2, 

 so that 



fid n= — (a2 _ JS^ gin „ 



ix'dfi. 



and for 



« = 0 , /X = a. 



B= fV^'V 



J6 V/x^-cV 



Hence, since is independent of r, we have 



C\dr= r ^-^-^ , C\^^-r^)hlr. 



Substituting 



■we have 



r = /Asin <^ 

 dr = ix, cos ^> d^, 



J6 (a^-,.,i(,a_,.)i,,._,.)f J -^7* 



or piitting 



we have 



. -lb 

 sm - 



/ (/x) iJ.^ dfx 



or, since the variable is of no consequence in a definite integral, wo get 

 f\dr= r f(^)^'dX ^^^^ 



