Definite Integration Question 457
Question: $ \int_0^{\pi /2}{|\sin x-\cos x|dx=} $
[Roorkee 1990; MP PET 2001; UPSEAT 2001]
Options:
A) 0
B) $ 2(\sqrt{2}-1) $
C) $ \sqrt{2}-1 $
D) $ 2(\sqrt{2}+1) $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \int_0^{\pi /2}{|\sin x-\cos x|dx} $
$ =\int_0^{\pi /4}{-(\sin x-\cos x})dx+\int _{\pi /4}^{\pi /2}{(\sin x-\cos x)dx}=2(\sqrt{2}-1) $ .
BETA
