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Question

Area bounded by the curve y=cot1x,y=tan1x and y-axis is equal to 
  1. π/40tanx dx+π/2π/4cotx dx 
  2. π/40tan1x dx  0π/4cot1x dx 
  3. 2ππ/20ln(sinx) dx
  4. 10tan1x dx 


Solution

The correct options are
A π/40tanx dx+π/2π/4cotx dx 
C 2ππ/20ln(sinx) dx

Required area=π/40tany dy+π/2π/4coty dy
=ln2+ln2
=ln2

π/40tan1x dx  0π/4cot1x dx=π28

2ππ/20lnsinx dx=I2I=2ππ/20lnsin2xdxln2dx, 2x=tI=ln2

I=tan1x dx=xtan1xx1+x2dx=xtan1x12ln(1+x2)10tan1x dx=π4ln22

 

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