First, let us find the intersection points of the curve,
Given Equations are x2 + y2 = 4 and x2 + y2 – 4x = 0.
From both of the equations,
4x = 4
x = 1
Putting this value in x2 + y2 = 4, we get,
1 + y2 = 4
y2 = 3
y = ±√3
Thus the curves intersect at A(1, √3) and B(1, - √3)
The area to be found is shaded in the figure above.
Area of Shaded region
Area of Shaded region \(=2\frac{\pi}{3}\) square units.