Definite Integration Question 390
Question: The value of $ \int _{0}^{1}{\frac{dx}{x+\sqrt{1-x^{2}}}} $ is
[MP PET 2003]
Options:
A) $ \frac{\pi }{3} $
B) $ \frac{\pi }{2} $
C) $ \frac{1}{2} $
D) $ \frac{\pi }{4} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ \int_0^{1}{\frac{dx}{x+\sqrt{1-x^{2}}}=\int_0^{\pi /2}{\frac{\cos \theta d\theta }{\sin \theta +\cos \theta }}} $
$ =\frac{\pi }{4} $ , (Put $ x=\sin \theta ,dx=\cos \theta d\theta $ ).
BETA
