Using integration find the area of the region bounded by the curve , x2 + y2 – 4x = 0 and the x-axis.
First, let us find the intersection points of the curve,
Given Equations are x2 + y2 = 4 and x2 + y2 – 4 x = 0.
From both of the equations,
4 x = 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 = square units.