Draw a rough sketch of the region {(x, y) : y2 ≤ 3x, 3x2 + 3y2 ≤ 16} and find the area enclosed by the region using method of integration.
To find area of region{(x, y) : y2 ≤ 3x, 3x2 + 3y2 ≤ 16}
The given equations are,
y2 = 3x ...(i)
And 3x2 + 3y2 = 16
...(ii)
Equation (i) represents a parabola with vertex (0,0) and axis as x - axis,
Equation (ii) represents a circle with centre (0,0) and radius 4/√3 and meet at A 
and B 
A rough sketch of the region
is drawn below
Required area = Region OCBAO
= 2(area of Region)
= 2(area of Region OBAO)
= 2(area of Region ODAO + area of Region DBAD)
The area enclosed by the region is 
13