Area bounded by two circles $x^2 + y^2 = 1, x^2 + (y-1)^2 = 1$ Consider the area enclosed by two circles: $x^2 + y^2 = 1, x^2 + (y-1)^2 = 1$
Calculate this area using double integrals:
I think I have determined the region to be $D = \{(x,y)| 0 \leq y \leq 1, \sqrt{1-y^2} \leq x \leq \sqrt{1 - (1-y)^2}\}$
Now I can't seem to integrate this. Is this region wrong? Should the integral just be $\int_0^1 \int_{\sqrt{1-y^2}}^{\sqrt{1- (1-y)^2}} dx dy$?
Do I need to convert this to polar form?

Solve the system: $x^2 + y^2 = 1 = x^2 + (y - 1)^2$ we have: $x =\dfrac{\sqrt{3}}{2}$ and $y = \dfrac{1}{2}$, and $x = -\dfrac{\sqrt{3}}{2}$ and $y = \dfrac{1}{2}$. So the set up for the integral is:$\int_\frac{-\sqrt{3}}{2}^{\frac{\sqrt{3}}{2}} \int_{1 -\sqrt{1 - x^2}}^{\sqrt{1 - x^2}} 1dydx$ which can be easily computed.
