Question

Find the area of the region in the first quadrant enclosed by X _axis . Line X=√3y and circle x$x^{2}$+ y$x^{2}$= 4

Answer 1

Answer

The equation of the circle

X^2 + y^2 = 4

Differentiate with respect to X

2X + 2y dy/dx = 0

While we differentiate 4 it is constant and it become zero

dy/dx =-x/y => (dy/dx) (1,√3) = -1/√3

y-√3 = -1/√3 (X-1)

X+ √3y = 4

And y =√3

A= ∫1 to° Y1dx + ∫° to 4 Y2dx

A= ∫√3 dx + ∫ 4-x/√3  dx

A = √3 [x²/2]1 to 0 + 1/√3 [4x-x²/2] 4 to 1

A= [√3/2+ 3√3/2 ]

= 2√3 sq units