Definite Integration Question 201
Question: $ \int_0^{\pi /2}{\frac{\cos x-\sin x}{1+\sin x\cos x}}dx= $
[Karnataka CET 2004]
Options:
A) 2
B) $ -2 $
C) 0
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ \int_0^{\pi /2}{\frac{\cos x-\sin x}{1+\sin x\cos x}dx=I} $ ……(i) Now $ I=\int_0^{\pi /2}{\frac{\cos ( \frac{\pi }{2}-x )-\sin ( \frac{\pi }{2}-x )}{1+\sin ( \frac{\pi }{2}-x )\cos ( \frac{\pi }{2}-x )}dx} $
= $ \int_0^{\pi /2}{\frac{\sin x-\cos x}{1+\sin x\cos x}dx} $
…..(ii) On adding, $ 2I=0\Rightarrow I=0 $ .
BETA
