Find the area enclosed by the parabola 4y = 3x 2 and the line 2y = 3x + 12.

Question

Philoid · Accepted Answer

We can see from the figure that the area of the region bounded by the curve 4y = 3x² 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)

⇒

= 45 -18

= 27 units.

Find the area enclosed by the parabola 4y = 3x2 and the line 2y = 3x + 12.

Find the area enclosed by the parabola 4y = 3x² and the line 2y = 3x + 12.