Definite Integration Question 271
Question: $ \int _{0}^{1}{\frac{d}{dx}[ {{\sin }^{-1}}( \frac{2x}{1+x^{2}} ) ]dx} $ is equal to
[Kerala (Engg.) 2002]
Options:
A) 0
B) $ \pi $
C) $ \pi /2 $
D) $ \pi /4 $
Show Answer
Answer:
Correct Answer: C
Solution:
$ I=[ {{\sin }^{-1}}( \frac{2x}{1+x^{2}} ) ]_0^{1}={{\sin }^{-1}}(1)-{{\sin }^{-1}}(0) $
$ =\frac{\pi }{2} $ .
BETA
