Definite Integration Question 26
Question: $ \int_0^{\pi /2}{\frac{\sin x}{\sin x+\cos x}dx} $ equals
[RPET 1996; Kerala (Engg.) 2002]
Options:
A) $ \frac{\pi }{2} $
B) $ \frac{\pi }{3} $
C) $ \frac{\pi }{4} $
D) $ \frac{\pi }{6} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ I=\int_0^{\pi /2}{\frac{\sin x.dx}{\sin x+\cos x}}=\int_0^{\pi /2}{\frac{\cos x.dx}{\cos x+\sin x}} $ , $ ( \because \int_0^{a}{f(x)dx=\int_0^{a}{f(a-x)dx}} ) $
$ 2I=\int_0^{\pi /2}{dx}\Rightarrow I=\frac{\pi }{4} $ .
BETA
