The area (in sq. units) of the portion lying above the X -axis and enclosed between the curves y^2=2 a x-x^2 and y^2=a x is

Step-by-step solution

Equation of given curves x^2+y^2-2 a x=0 and y^2=a x Area of the portion lying above the X -axis and enclosed between the given curves, from the diagram is ₀^a ( 2 a x-x^2 - a x ) d x= ₀^a a^2-(x-a)^2 d x- a ₀^a x^ 1 / 2 d x= [ x-a 2 2 a x-x^2 + a^2 2 ⁻¹ ( x-a a )- a 2 x^ 3 / 2 3 ]₀^a=- 2 3 a^2+ 2 a^2 2 =a^2 ( 4 - 2 3 ) sq units