The circle x² + y² - 2x = 0 is divided into two parts by the line y = x. Let A₁ and A₂ respectively be the areas of the major and minor parts. What is the value of A₁?

The circle is (x-1)² + y² = 1, center (1, 0), radius 1, total area π. The line y = x cuts through. Distance from center (1,0) to line y = x (i.e., x - y = 0) is |1-0|/√2 = 1/√2. The line cuts the circle at (0,0) and (1,1). The chord subtends angle 2·arccos(1/√2)/... actually the central angle: points (0,0) and (1,1) from center (1,0): vectors (-1,0) and (0,1), angle = 90° = π/2. The minor segment area = (1/2)r²(θ - sin θ) = (1/2)(1)(π/2 - 1) = (π-2)/4. So A₂ = (π-2)/4, and A₁ = π - (π-2)/4 = (4π - π + 2)/4 = (3π + 2)/4.