JEE Main On 8 April 2017 Question 30
Question: The integral $ \int _{{}}^{{}}{\sqrt{1+2\cot x(cosecx+cotx)}dx} $ $ ( 0<x<\frac{x}{2} ) $ is equal to : (where C is a constant of integration ) [JEE Online 08-04-2017]
Options:
A) $ 2\log ( \sin \frac{x}{2} )+C $
B) $ 4\log ( \sin \frac{x}{2} )+C $
C) $ 4\log ( \cos \frac{x}{2} )+C $
D) $ 2\log ( \cos \frac{x}{2} )+C $
Show Answer
Answer:
Correct Answer: A
Solution:
- $ \int _{{}}^{{}}{( \sqrt{+2\cot x\cos ecx+\cos ec^{2}x+\cot x} )dx} $
$ \int _{{}}^{{}}{\cos |x+\cot x|dx} $
$ \int _{{}}^{{}}{(cosec+cotx)dx} $
$ \int _{{}}^{{}}{\frac{1+\cos x}{\sin x}}dx$
$ \int _{{}}^{{}}{\cot{\frac{x}{2}}}dx$
$ 2\log (\sin(\frac{x}{2}))+c $
