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Question: Answered & Verified by Expert
0π4x.sec2xdx= 
MathematicsDefinite IntegrationMHT CETMHT CET 2018
Options:
  • A π4+log2
  • B π4-log2
  • C 1+log2
  • D 1-12log2
Solution:
2932 Upvotes Verified Answer
The correct answer is: π4-log2
Integrating by parts
0 π 4 x sec 2 xdx = ( x sec 2 xdx ) 0 π 4 0 π 4 ( d dx ( x ). sec 2 x dx )dx
= ( xtanx ) 0 π 4 0 π 4 tanxdx
I = x tan x - n sec x 0 π 4 = π 4 1 - n 2
= π 4 - log 2

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