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Calculus Level 2

G= ∫ 0 π / 2 log ⁡ ( t a n x ) ∂ x \int _{ 0 }^{ \pi /2 }{ \log { (tan\quad x) } } \partial x Then, find G?


The answer is 0.

Varun Suvarna by Varun Suvarna , 23, India

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1 solution

Ramesh Goenka
Oct 23, 2014

replace x by pi/2 - x ... add the two .. we get 0 .. !

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its a question from the topic indefinite integral its a property of integral that if the limit tends from 0 to a we can replace the f(x) as f(a-x). in this case we replace tan x by tan(pi/2-x) and it becomes cotx now the question becomes integration of lncotx and adding the two integrals ln tanx and ln cotx we get 2G=ln1 which means g=0

Kumar Arpit - 6 years, 7 months ago

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