Q. 94.2( 75 Votes )

Find the area of the region bounded by the parabola y = x2 and y=|x|.

Answer :

It is given that the area of the region bounded by the parabola y = x2 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 = x2 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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