The area (in sq units) of the region {(x ,y ): y^2 =2x and x^2+y^2 =4x, x =0, y - Maths - Application of Integrals

Question

The area (in sq units) of the region {​(x ,y ): y^2>=2x
and x^2+y^2<=4x, x>=0, y>=0} is

Rahul Raj · Accepted Answer

dear student

the area y2≥2x, represents the area outside the parabola y2=2xthe area x2+y2≤4x, represents the area inside the circle (x-2)2+y2=22 parabola y2=2x and the circle (x-2)2+y2=22intersect at (2,2), found out by solving the two equation simultaneouslyso, required area is the area between the two curves in the first quadrant as it is given that both x and y >0A=∫024x-x2-2xdx=∫024-x-2)2-2xdx=12(x-2)4-x-2)2+4sin-1x-22-223x3/202=π-83

regards

The area (in sq. units) of the region {​(x ,y ): y^2>=2x and x^2+y^2<=4x, x>=0, y>=0} is

The area (in sq. units) of the region {(x ,y ): y^2>=2x and x^2+y^2<=4x, x>=0, y>=0} is