Q. 94.2( 65 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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