FOURIER'S THEOREM 



function represented by the first three terms on the right hand 



is so slight that it would be barely perceptible on a scale 



suited to the pages of this book. 



In the next example the graph of f(x) consists of two straight 



lines through the points x = 0, x = TT, respectively, meeting at 



an angle at the point x = a. If we assume the ordinate at the 



latter point to be unity, we have 



/(*) = #/ [0 <*<], j 



/(#) = (TT - at) / (IT -a) [*<*<*].) 



We find, after some reductions, 



2 f a 2 f 71 " 



A 8 xsinsxdx-\ -- -. -- ^1 (TT x) sin sx dx 

 Tra.'o 7r(7r-a)J a 



1 



-sinsa. ...(11) 





a(7r-a) V 



Fig. 35. 



