Definite Integration Question 454
Question: The correct evaluation of $ \int_0^{\pi /2}{| \sin ( x-\frac{\pi }{4} ) |dx} $ is
[MP PET 1993]
Options:
A) $ 2+\sqrt{2} $
B) $ 2-\sqrt{2} $
C) $ -2+\sqrt{2} $
D) 0
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ I=\int_0^{\pi /2}{| \sin ( x-\frac{\pi }{4} ) |}dx $
$ x-\frac{\pi }{4} $ is -ve when $ x\le \frac{\pi }{4} $ and +ve when $ x>\frac{\pi }{4} $
$ =-\int_0^{\pi /4}{\sin ( x-\frac{\pi }{4} )dx+\int _{\pi /4}^{\pi /2}{\sin ( x-\frac{\pi }{4} )dx}} $
$ =2-\sqrt{2} $ .
BETA
