JEE Main 2014MathematicsIndefinite IntegrationHardMCQ

JEE Main 2014 — Indefinite Integration Question with Solution

JEE Main 2014 (09 Apr Online)

Question

∫sin8x-cos8x1-2sin2xcos2xdx is equal to 

Choose an option

Show full solutionCorrect option: A
Correct answer
A-12sin2x+c

Step-by-step explanation

sin8x-cos8x=sin2x-cos2xsin2x+cos2xsin4x+cos4x

and sin4x+cos4x=sin2x+cos2x2-2sin2xcos2x=1-2sin2xcos2x

∴I=∫sin8x-cos8x1-2sin2xcos2xdx

=∫sin2x-cos2xsin4x+cos4xsin4x+cos4xdx

 =-∫cos2xdx 

  =-12sin2x+c, where c is the constant of integration.  

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About this question

This is a previous-year question from JEE Main 2014, covering the Indefinite Integration chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.