
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 $\displaystyle r = sin(\theta)$ and $\displaystyle r = cos(\theta)$
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 $\displaystyle r = sin(\theta)$ and did the integral $\displaystyle 2* \frac12 \int_0 ^\frac\pi4 sin^2(\theta)d\theta$ I would get the area bounded between the two circles. In the end I got $\displaystyle \frac\pi8  \frac14$
Could someone tell me if I am correct. Thank you.

That answer is correct for the integral given.

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.

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.

