Definite-Integration Question 514
Question: $ \int_0^{\infty }{\frac{x,dx}{(1+x)(1+x^{2})}}= $
Options:
A) $ \frac{\pi }{4} $
B) $ \frac{\pi }{3} $
C) $ \frac{\pi }{6} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ I=\int_0^{\infty }{\frac{xdx}{(1+x)(1+x^{2})}} $ Put $ x=\tan \theta $ , we get $ I=\int_0^{\pi /2}{\frac{\tan \theta }{1+\tan \theta }d\theta =\int_0^{\pi /2}{\frac{\sin \theta }{\cos \theta +\sin \theta }d\theta =\frac{\pi }{4}}} $ .
BETA
