INTEGRATION 145 



fcos0d0 



( b ) 4Q Let - sin 



J sin 4 



dx 

 and -jx = cos 



or dx = cos d6 



Cdr C 

 The integral becomes I = la;- 4 dx 



r 



J 



3 sin 3 



- 7* + 12 



and -^ = 10* - 7 



The integral becomes I j= = |?/~ 



or dy = (lOa; 7) dx 

 j= 



* 



= 2V5x*-7x+ 12 



and T 2 - = sec 2 x 

 dx 



or dy = sec 2 # da? 



The integral becomes l-^ = \y~ z dy 

 j y j 



1 



tan a? 



88. The Integration of Algebraic Fractions whose Denominators 

 split up into Linear Factors. In this case the fraction can be 

 split up into its partial fractions, and then each partial fraction 

 can be integrated separately. 



K 



