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∫ -a a e ax cosnxdx

∫-aaeaxcosnxdx

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1 Answers

abhishek singh
40 Points
8 years ago
see , you have to  use by parts.. 
.. for simplification put “ nx “ = “t” … then dx = dt/n , and eax = e(a/n)*t
 now ,  Take  COSt as the first part and e(a/n)*t as the second part .. 
 I =∫-aaeaxcosnxdx
 i.e    
 
I =( cost ) * ( e(a/n)*t  )*( n/a )  +  ∫( sint )  * (  e(a/n)*t )* ( n/a )dt   ------------> {1}
                                         = again taking ( sint) as the first part and the other one as second part  we can write the later term including integration sign as  
  ( sint ) *  (  e(a/n)*t )* ( n/a )* ( n/a ) –  ∫(cost) *  (  e(a/n)*t )* ( n/a )* ( n/a ) dt
 = ( sint ) *  (  e(a/n)*t )* ( n/a )* ( n/a )  – I* ( n/a )* ( n/a )  
  now put this  value in  equation number {1} . and then solve urselve to get the answer  
(a2 /n)*(1/ (a2 + n2 ) )*[eax ] * ( acosnx + nsinnx )

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