<p>The area of the region consisting of all points \((x, y)\) so that \(x^2 + y^2 \leq 1\) and \(|x| + |y| \leq 1\) is</p>
Step-by-Step Solution
Key Concept: Find the intersection of a circle and a diamond-shaped region; use symmetry and integration to compute the overlap area.
<p>The region is the intersection of the unit circle $x^2 + y^2 \leq 1$ and the square $|x| + |y| \leq 1$. The square has vertices at $(\pm 1, 0)$ and $(0, \pm 1)$ with area 2. By symmetry and integration, the area of intersection equals $\pi - 1$.</p>
Correct Answer: B