Prove that the area common to the two parabolas y = 2x2 and y = x2 + 4 is 32/3 sq. Units.

To find the area enclosed by,

y = 2x2 ...(i)


And y = x2 + 4 ...(ii)


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


2x2 = x2 + 4


Or x2 = 4


Or x =


y = 8


Equation (1) represents a parabola with vertex (0,0) and axis as y - axis.


Equation (2) represents a parabola with vertex (0,4) and axis as the y - axis.


Points of intersection of parabolas are A(2,8) and B( – 2,8).


These are shown in the graph below: -



Required area = Region AOBCA


= 2(Region AOCA)







Hence, proved that the area common to the two parabolas y = 2x2 and y = x2 + 4 is 32/3 sq. Units.


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