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