Definite Integration Question 400
Question: The value of $ \int_0^{\pi /4}{\frac{1+\tan x}{1-\tan x}dx} $ is
[SCRA 1986]
Options:
A) $ -\frac{1}{2}\log 2 $
B) $ \frac{1}{4}\log 2 $
C) $ \frac{1}{3}\log 2 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ \int_0^{\pi /4}{\frac{1+\tan x}{1-\tan x}dx=\int_0^{\pi /4}{\tan ( \frac{\pi }{4}+x )dx}} $
$ =[ \log { \sec ( \frac{\pi }{4}+x ) } ]_0^{-\pi /4}=-\frac{1}{2}\log 2 $ .
BETA
