Definite Integration Question 500
Question: The sine and cosine curves intersects infinitely many times giving bounded regions of equal areas. The area of one of such region is
[DCE 2005]
Options:
A) $ \sqrt{2} $
B) $ 2\sqrt{2} $
C) $ 3\sqrt{2} $
D) $ 4\sqrt{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
Point of intersection of y=sinx and $ y=\cos x $ are $ \frac{\pi }{4}, $
$ \frac{\pi }{4},\frac{5\pi }{4} $ .
Since, $ \sin x\ge \cos x $ on the interval $ [ \frac{\pi }{4},\frac{5\pi }{4} ] $
$ \therefore $ Area of one such region $ =\int _{\pi /4}^{5\pi /4}{(\sin x-\cos x)\ dx} $
$ =2\sqrt{2}sq.\ unit $ .
BETA
