JEE Main Solved Paper 2017 Question 15
Question: The integral $ \int\limits _{\frac{\pi }{4}}^{\frac{3\pi }{4}}{\frac{dx}{1+cos,x}} $ is equal to:- [JEE Main Solved Paper-2017]
Options:
A) -1
B) -2
C) 2
D) 4
Show Answer
Answer:
Correct Answer: C
Solution:
$ I=\int\limits _{\frac{\pi }{4}}^{\frac{3\pi }{4}}{\frac{dx}{1+\cos x}} $ .. [a]
$ I=\int\limits _{\frac{\pi }{4}}^{\frac{3\pi }{4}}{\frac{dx}{1-\cos x}} $ .. [b]
Adding and $ 2I=\int\limits _{\frac{\pi }{4}}^{\frac{3\pi }{4}}{\frac{2}{{{\sin }^{2}}x}}dx $
$ I=\int\limits _{\frac{\pi }{4}}^{\frac{3\pi }{4}}{\cos ec^{2}x,dx} $ $ I=-(\cot x) _{\pi /4}^{3\pi /4}=2 $
