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

\(\frac{3π}{4}\ + \frac{1}{2}\)

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.