Find the area of the region (x,y): x² + y² ≤ 4, x + y ≥ 2

x² + y² ≤ 4 denotes the area inside the circle, whose center is (0,0) and radius is 2 units. The inequality x + y ≥ 2 denotes the region on the right-hand side of the line x + y = 2, and the line intersects the coordinate axes at (0,2) and (2,0). This can be obtained by subtracting the area of a quarter circle and the right-angled triangle which forms. Therefore, π × r²/4 - ½ × r × r is the required area, where r is the radius of the circle. = π × 4/4 - ½ × 2 × 2 = π - 2 ≈ 1.142 square units.