## Book: RD Sharma - Mathematics (Volume 2)

### Chapter: 21. Areas of Bounded Regions

#### Subject: Maths - Class 12th

##### Q. No. 25 of Exercise 21.3

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25
##### Find the area of the region in the first quadrant enclosed by the x - axis, the line y = √3x and the circle x2 + y2 = 16.

To find the area enclosed by

y = √3x ...(i)

x2 + y2 = 16 ...(ii)

On solving the equation (i) and (ii),

Or x2 + = 16

Or 4x2 = 16

Or x2 = 4

Or x =

Y = ±

Equation (i) represents a parabola with vertex (0,0) and axis as x - axis.

Equation (ii) represent axis a circle with centre (4,0) and meets axes at (0,0) and (4,0).

They intersect at A (2,) and C ( – 2, – ).

These are shown in the graph below: -

Area of the region OAB = Area OAC + Area ACB

The area of the region in the first quadrant enclosed by x - axis, the line y = √3x and the circle x2 + y2 = 16 is

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