The line y = x, partition the area of the circle (x – 1)2 + y2 = 1, into two segments. The area of the major segment is

\(\frac{π}{2}\ + \frac{1}{4}\) \(\frac{π}{4}\ + \frac{1}{2}\) \(\frac{3π}{4}\ + \frac{1}{6}\) \(\frac{3π}{4}\ + \frac{1}{2}\)

\(\frac{3π}{4}\ + \frac{1}{2}\)

At point of intersection y = x $⇒ (x - 1)^2 + x^2 = 1$ $⇒ 2x^2-2x=0$ $⇒ 2x(x - 1) = 0$ x = 0, x = 1 y = 0, y = 1 Area of major portion $=\frac{3}{4}×π(1)^2+\frac{1}{2}×1×1$ $=\frac{3π}{4}+\frac{1}{2}$ Option D is correct.