Question

The area of the region lying above X-axis, and included between the circle x² + y² = 2ax and the parabola y² = ax, a > 0 is ______ 

Options

• 8πa² 

• `a^2(pi/4 - 2/3)`

• `(16pia^2)/9`

• `pi(27/8 + 3a^2)`

Answer 1

The area of the region lying above X-axis, and included between the circle x² + y² = 2ax and the parabola y² = ax, a > 0 is `underline(a^2(pi/4 - 2/3))`.

Explanation: 

Required area = `(pia^2)/4 - int_0^a sqrt(ax)dx`

= `(pia^2)/4 - (2sqrta)/3 [x^{3/2}]_0^a` 

= `(pia^2)/4 - (2a^2)/3`

= `a^2(pi/4 - 2/3)` sq. units