What is the area of the smaller region cut off from the circle $x^{2} + y^{2} = 4$ by the line $x + y = 2$?

Explanation

1. 01

   The line meets the circle at $(2, 0)$ and $(0, 2)$: the region is the quarter circle minus the triangle under the line.

2. 02

   $\int_0^{2} \left(\sqrt{4 - x^{2}} - (2 - x)\right)dx = \pi - 2$ square units.