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Find the area enclosed by the parabolas y = 5x2 and y = 2x2 + 9.
To find the area enclosed by
y = 5x2 ...(i)
and y = 2x2 + 9 ...(ii)
On solving the equation (i) and (ii),
5x2 = 2x2 + 9
Or 3x2 = 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 = 5x2 and y = 2x2 + 9 is