Definite Integration Question 94
Question: $ \int_0^{\pi /2}{\frac{\cos x}{(1+\sin x)(2+\sin x)}}dx= $
[UPSEAT 1999]
Options:
A) $ \log \frac{4}{3} $
B) $ \log \frac{1}{3} $
C) $ \log \frac{3}{4} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Put $ \sin x=t\Rightarrow \cos xdx=dt, $ so that reduced integral is $ \int_0^{1}{( \frac{1}{1+t}-\frac{1}{2+t} )dt=[\log (1+t)-\log (2+t)]_0^{1}} $
$ =\log \frac{2}{3}-\log \frac{1}{2}=\log \frac{4}{3} $ .
BETA
