Question

Using integration, find the area of the region {(x, y) : x² + y² ≤ 2ax, y² > ax, x,y, ≥ 0}

Answer 1

{(x, y) : x² + y² ≤ 2ax, y² > ax, x,y, ≥ 0}

Considering the inequations as equations

It represents a circle whose Centre is (a, 0) and radius r = a

y²  = ax..........(iii)

Vertex (0,0) Axis along x-axis.

Point of intersection, from (i) and (iii)

Point of intersection are (0, 0) (a, a), (a, -a).