The graphs of the circles $x^2 + y^2 = 2$ and $(x-1)^2 + y^2 = 1$ intersect at the points $(1,1)$ and $(1,-1)$. Let $R$ be the shaded region in the first quadrant bounded by the two circles and the $x$-axis. (a) Set up an expression involving one or more integrals with respect to $x$ that represents the area of $R$. (b) Set up an expression involving one or more integrals with respect to $y$ that represents the area of $R$. (c) The polar equations of the circles are $r = \sqrt{2}$ and $r = 2\cos\theta$, respectively. Set up an expression involving one or more integrals with respect to the polar angle $\theta$ that represents the area of $R$.
The graphs of the circles $x^2 + y^2 = 2$ and $(x-1)^2 + y^2 = 1$ intersect at the points $(1,1)$ and $(1,-1)$. Let $R$ be the shaded region in the first quadrant bounded by the two circles and the $x$-axis.
(a) Set up an expression involving one or more integrals with respect to $x$ that represents the area of $R$.
(b) Set up an expression involving one or more integrals with respect to $y$ that represents the area of $R$.
(c) The polar equations of the circles are $r = \sqrt{2}$ and $r = 2\cos\theta$, respectively. Set up an expression involving one or more integrals with respect to the polar angle $\theta$ that represents the area of $R$.