Q. 94.2( 65 Votes )

# Find the area of the region bounded by the parabola y = x^{2} and y=|x|.

Answer :

It is given that the area of the region bounded by the parabola y = x^{2} and y = |x|.

Now, we can observed that the given area is symmetrical about y-axis.

⇒ Area OACO = Area ODBO

And the point of intersection of parabola, y = x^{2} and y = x is A (1, 1).

Thus, Area OACO = Area ΔOAM – Area OMACO

Now, Area of ΔOAM =

Area of OMACO =

⇒ Area OACO = Area ΔOAM – Area OMACO

=

Therefore, the required area is = 2(1/6) = 1/3 Answer.

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