Test Index

NIMCET 2012 Question Paper with solutions

Question : 9 of 120

Marks: +1, -0

\int\limits_{0}^{\frac{\pi}{2}}

log tan x dx is

Solution:

Let I =

\int\limits_{0}^{\frac{\pi}{2}}

log tan x dx ... (i)

Use definite integeral property

I =

\int\limits_{0}^{\frac{\pi}{2}}

log tan

\left(\frac{\pi}{2}-x\right)

\int\limits_{0}^{\frac{\pi}{2}}

log cot x dx ... (ii)

On adding Eqs. (i) and (ii),

2I =

\int\limits_{0}^{\frac{\pi}{2}}

(log tan x + log cot x) dx (Since log m + log n = log mn)

\int\limits_{0}^{\frac{\pi}{2}}

log (tan x . cot x) dx

\int\limits_{0}^{\frac{\pi}{2}}

log 1 dx

\int\limits_{0}^{\frac{\pi}{2}}

0 dx

= 0

Go to Question:

Prev Question

Next Question