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question mark

​The value of the integral
π/3
∫ ((x sin x ) / (cos2x )) dx , is
-π/3
  1. (π/3 – log tan 3 pi/2)
  2. 2( 2pi/3- log tan 5pi/12)
  3. 3(pi/2-log sin pi/12)
  4. none of these

sun , 6 Years ago
Grade 12
anser 1 Answers
Sushant Kumar

Last Activity: 6 Years ago

answer is 
  1. 2( 2pi/3- log tan 5pi/12)
 
 
π/3
  ∫    ((x sin x ) / (cos2x )) dx , is = -π/3
π/3
  ∫    ((x tanx secx )) dx   now take tanxsecx as 1ST  function and x as 2nd function as integration of tanxsecx is secx  
-π/3
 now take tanxsecx as 1ST  function and x as 2nd function as integration of tanxsecx is secx and diferentiation of x is dx
 
using integration by parts you will get the answer ( value of tan(5pi/12/)=2+sqrt(3)  )
 
hope this will help 

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