Question

The area bounded by the curves $y=\cos x,y=\cos 2x$ between the ordinates $x=0,x=\frac{\pi }{3}$ are in the ratio

• A. $2\sqrt{3}:4-\sqrt{3}$
• B. $2:1$
• C. $2\sqrt{3}:4+\sqrt{3}$
• D. $1:3$

Answer 1

The correct option is A $2\sqrt{3}:4-\sqrt{3}$

$y=\cos x,y=\cos 2x$
$\stackrel{\pi /3}{\underset{0}{\int }}\left(\cos x\right)dx$ area of $\cos x$ and area of $\cos 2x$
$\stackrel{\pi /4}{\underset{0}{\int }}\left(\cos 2x\right)dx-\stackrel{\pi /3}{\underset{\pi /4}{\int }}\left(\cos 2x\right)dx=\frac{4-\sqrt{3}}{4}$
$\stackrel{\pi /3}{\underset{0}{\int }}\left(\cos x\right)dx=\frac{\sqrt{3}}{2}squnits$
S0, ratio is $\frac{\sqrt{3}}{2}:\frac{4-\sqrt{3}}{4}=2\sqrt{3}:4-\sqrt{3}$