How to integrate log (1+tan (x)) from 0 to π ? Is the function even or odd or neither?
Adarsh Khandelwal , 8 Years ago
Grade 12th pass
Integral Calculus> How to integrate log (1+tan (x)) from 0 t...
1 AnswersNandana
Last Activity: 8 Years ago
this below fig. shows the integration which we want
as we can see that , this integration is not converging it goes to infinite
we can show it by doing integration also
let’s take ∫0pi (1+tan x) dx = ∫0pi dx + ∫0pi tan x dx = π + ∫0pi sin x / cos x dx
= π + mod(∫01 1/ u du) +mod ( ∫-10 1/ u du) [ take u= cos x , then
du = -sinx dx ]
= π + ln (0)+ ln(0) → infinite
and it is neither even nor odd in this intervel as we can see .
Thank you .
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