# Finding area between curves?

• May 22nd 2011, 03:23 PM
dorkymichelle
Finding area between curves?
Find the area of the region of
y= cos x and y=sin2x, x= 0, x=pi/2
i sketched the curve and y=cos x is on top, so wouldn't it be
\int cosx-sin2x from pi/2 to 0?
• May 22nd 2011, 03:43 PM
Mondreus
Are you sure that $\cos x \geq \sin{2x}$ on $x\in[0,\pi/2]$?

What about $x=\pi/4$? You need to break up the integral into intervals where one function is greater than or equal to the other.
• May 22nd 2011, 03:48 PM
dorkymichelle
so would I have to split it into 2 integrals, one where cos x is bigger than sin2x, and the other where sin2x is bigger than cos x?
• May 22nd 2011, 03:51 PM
Mondreus
Yes. In order to do that you need to solve $\cos x = \sin{2x}\Leftrightarrow \cos x = 2\cos x \sin x$