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value of ∫dx/√3 sinx+cosx is equal to=? give the process of it also.plz reply soon!

value of ∫dx/√3  sinx+cosx is equal to=? give the process of it also.plz reply soon!

Grade:12

1 Answers

Arun
25758 Points
3 years ago
 

Multiply and divide by 2. 

 I= dx/root(3) sinx+cosx

  then 2I= dx/(root(3)/2 *sinx + (cosx)/2 ) 

 then root(3)/2=cos30 1/2 = sin 30

 

then root(3)sinx+ cosx becomes  2sin(30+x) .  then the integration becomes integration of cosec(x+30) multiplied by 1/2. 

 which equals  [log(tan(x+30)/2))] . 1/2+constant. 

 

Regards

Arun (askIITians forum expert)

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