# Thread: area enclosed by cardiod.

1. ## area enclosed by cardiod.

r = 1 + sin(theta)

i know the integral equation should be: 1/2 integral pi/6 -> pi/2 ( 1 + sin(theta) + sin^2(theta) )

just need help solving through the integral please.

thanks.

2. ## Integral

Hello rcmango
Originally Posted by rcmango
r = 1 + sin(theta)

i know the integral equation should be: 1/2 integral pi/6 -> pi/2 ( 1 + sin(theta) + sin^2(theta) )

just need help solving through the integral please.

thanks.
To integrate the $\sin^2\theta$ term, use

$\cos 2\theta = 1 - 2\sin^2\theta$

in the form

$\sin^2\theta = \tfrac{1}{2}(1 - \cos 2\theta)$

and it's very straightforward from there.