Question
Draw a rough sketch of the region {(x, y): y2 ≤ 3 x, 3 x2 + 3 y2 ≤ 16} and find the area enclosed by the region using method of integration.
Solution
Given region is
Consider the equations
...(1)
i.e., 
...(2)
From (1) and (2), we get,
Rejecting negative values of x, we get
which gives the abscissa of the points of intersection P and Q.
Required area = Area of shaded region
= 2 [area of region APOA]
= 2 [area of region AMPA + area of region MOPM ]
= 
= 
