Answer :

We can see from the figure that the area of the region bounded by the curve 4y = 3x^{2} and the line 2y = 3x + 12 is shown by shaded region that is Area OBAO.

The points of intersection of both the curves are A(-2,3) and (4, 12).

Now draw AC and BD perpendicular to x – axis.

Thus,

Area of OBAO = Area CDBA – (Area ODBA + Area OACO)

⇒

⇒

⇒

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= 45 -18

= 27 units.

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