Definite Integration Question 95
Question: $ \int_0^{\pi /2}{{}}(\sin x-\cos x)\log (\sin x+\cos x)dx= $
[SCRA 1986]
Options:
A) $ -1 $
1
0
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Put $ \sin x+\cos x=t\Rightarrow -(\sin x+\cos x)dx=dt $
Also as $ x=0 $ to $ \frac{\pi }{2},t=1 $ to 2.
Since here limit is -1 to 1-, therefore the value of integral will be zero, $ { \because \int_{-1}^{1}{f(x)dx=0} } $ .
BETA
