Question

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

Answer 1

The area bounded by the parabola,x²=y and the line,y=|x|,can be represented as

The given area is symmetrical about y-axis.

∴Area OACO=Area ODBO

The point of intersection of parabola,x²=y,and line,y=x,is A(1,1).

Area of ΔOAB=1/2×OB×AB=1/2×1×1=1/2

Area of OBACO=∫10ydx=∫10x2dx=[x3/3]10=1/3

⇒Area of OACO=Area of ΔOAB-Area of OBACO

=1/2-1/3

=1/6

Therefore,required area=2[1/6]=1/3units.