Definite Integration Question 307
Question: Area between the curve $ y=\cos x $ and $ x- $ axis when $ 0\le x $ is
[MP PET 1997]
Options:
A) 2
B) 4
C) 0
D) 3
Show Answer
Answer:
Correct Answer: B
Solution:
$ y=\cos x $ , When $ x\in [ 0,\frac{\pi }{2} ],\cos x\ge 0 $
When $ x\in [ \frac{\pi }{2},\frac{3\pi }{2} ],\cos x\le 0 $
When $ x\in [ \frac{3\pi }{2},2\pi ],\cos x\ge 0 $
Thus required area is given by, $ \int_0^{\pi /2}{ydx}=\int_0^{\pi /2}{\cos xdx+\int _{\pi /2}^{3\pi /2}{(-\cos x)dx+\int _{3\pi /2}^{2\pi }{\cos xdx}}} $
$ =1+2+1=4sq. $ unit.
BETA
