Find the area of the region bounded by the parabola y = x 2 and y=|x|.

Question

Philoid · Accepted 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

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