Find the area enclosed by the parabolas y = 5x^{2} and y = 2x^{2} + 9.

To find the area enclosed by

y = 5x^{2} ...(i)

and y = 2x^{2} + 9 ...(ii)

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

5x^{2 =} 2x^{2} + 9

Or 3x^{2} = 9

Or x =

Or 15

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

Equation (ii) represents a parabola with vertex C (0, 9) and axis as the y - axis.

Points of intersection of parabolas are A (√3, 15) and B( – √3,15)

These are shown in the graph below: -

Required area = Region AOBCA

= 2(Region AOCA)

The area enclosed by the parabolas y = 5x^{2} and y = 2x^{2} + 9 is

21