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

y=|x|—(2)
Curve (i) is symmetrical about y-axis since it contains even power of x.
Solving (1) and (2), we get
Case 1: If x≥0, x²=x ⇒x(x−1)=0
Therefore, x=0, x=1
So, the point os intersections are (0, 0) and (1,1)
Case 2: If x≤0, x²=−x ⇒x(x+1)=0
Therefore x=0, x=−1
So, point of intersections are (0,0) and (−1,1).
Now required area =2×ar(OABCO)=2[∫₁₀y₂dx−∫₁₀y₁dx]=2[∫₁₀|x|dx−∫₁₀x²dx]=2[∫₁₀(x−x²)dx]=2[x²/2−x³/3]₁₀=2[1/2−(0)]=1/3
Therefore, the required area is 1/3 Sq.units.