# Area between two circles

• Apr 12th 2010, 08:18 PM
xwanderingpoetx
Area between two circles
I would like to know if my thinking on the problem is correct. I need to find the area between the circles $r = sin(\theta)$ and $r = cos(\theta)$

After I graphed the 2 circles I looked at them and realized that the area between them is symmetric so I only need to find one half of it and multiply it by 2. So I figured that if I just took the circle $r = sin(\theta)$ and did the integral $2* \frac12 \int_0 ^\frac\pi4 sin^2(\theta)d\theta$ I would get the area bounded between the two circles. In the end I got $\frac\pi8 - \frac14$

Could someone tell me if I am correct. Thank you.
• Apr 12th 2010, 08:31 PM
dwsmith
That answer is correct for the integral given.
• Apr 12th 2010, 08:38 PM
xwanderingpoetx
I know that the integral is correct, but I would like to know if my thinking that lead to that integral is correct as well.
• Apr 12th 2010, 08:40 PM
dwsmith
I believe so. I know I answered this question a month or so ago but I can't remember what the outcome was.

Integrating the sin function from 0 to pi/4 is the right idea.

The answer is reasonable too so I think you have it.

The thread I did whenever is at physicsforums.com.
• Apr 12th 2010, 08:45 PM
dwsmith
• Apr 12th 2010, 08:51 PM
xwanderingpoetx
Awesome, thank you.