Calculate the area of the region between the circles x² + y² = 4 and (x – 2)² + y² = 4.

Area of the region bounded by the curve y=f(x), the x-axis and the ordinates x=a and x=b, where f(x) is a continuous function defined on [a,b], is given by .

Given; x² + y² = 4 and (x – 2)² + y² = 4

By solving; x² + 4 − (x – 2)² = 4

⇒ x² − x² + 4x − 4 = 0

∴ x = 1 is the point of intersection.

Required Area