**Area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle x2 + y2 … units (c) 32π sq. units …**

###### Answers:

(b) We have, y = 0, y = x and the circle x^{2} + y^{2 }= 3 in the first quadrant .

Solving y = x with the circle

x^{2 }+ x^{2} = 32

⇒ x^{2} = 16

⇒ x = 4

When x = 4, y = 4

For point of intersection of circle with the x-axis,

Put y = 0

∴ x^{2} + 0 = 32

⇒ x = ± 4√2

So, the circle intersects the x-axis at (± 4√2,0)

From the figure, area of shaded region