12th Class
Mathematics
Definite Integrals
Question Bank
Critical Thinking
question_answer
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]
A)\[\sqrt{2}\]
B)\[2\sqrt{2}\]
C)\[3\sqrt{2}\]
D)\[4\sqrt{2}\]
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 \[\left[ \frac{\pi }{4},\frac{5\pi }{4} \right]\] \[\therefore \] Area of one such region \[=\int_{\pi /4}^{5\pi /4}{(\sin x-\cos x)\ dx}\] \[=2\sqrt{2}sq.\ unit\].