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what will be its answer ..... its a bit confusing one.... ∫(Sin X 2 ) 2 .(CosX 2 ) 2 dx



what will be its answer .....


its a bit confusing one....


 ∫(Sin X2)2.(CosX2)dx



Grade:Upto college level

1 Answers

Askiitians Expert Soumyajit IIT-Kharagpur
28 Points
11 years ago

Dear Pawan deep,

Ans:- f(x)=∫(sinX²)²(cosX²)²dx

             =1/4∫(sin2X²)²dx

               =1/16∫(1 - cos4X²)²dx

                =1/16∫(1 - 2cos4X²+ cos²4X²)dx

                =1/16∫(3/2 - 2cos4X² +1/2cos8X²)

                  =3/32 X -1/8∫cos4X²dx +1/16 ∫cos8X²

Now the value of the 2nd and the third integral can not be found unless it is a definte integral.

 

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Regards,

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SOUMYAJIT IIT_KHARAGPUR

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