Definite Integration Question 384
The ratio of the areas bounded by the curves $ y=\cos x $ and $ y=\cos 2x $ between $ x=0 $ and $ x=\frac{\pi}{2} $
$ x=\pi /3 $ and $ x- $ axis, is
[MP PET 1997]
Options:
A) $ \sqrt{2}:1 $
B) $ 1:1 $
C) $ 1:2 $
D) $ 2:1 $
Show Answer
Answer:
Correct Answer: D
Solution:
$ A_1=\int_0^{\pi /3}{\cos xdx=\sin x|_0^{\pi /3}=\frac{\sqrt{3}}{2}} $ , $ A_2=\int_0^{\pi /3}{\cos 2xdx=\frac{1}{2}\sin 2x|_0^{\pi /3}=\frac{\sqrt{3}}{4}} $
$ A_1:A_2=2:1 $ .
BETA
