Find the area of the region included between the parabola and the line 3x – 2y + 12 = 0.

Given;

∴ By solving for point of intersection

⇒ 3x² − 6x − 24 = 0

⇒ x² − 2x − 8 = 0

⇒ (x − 4)(x + 2) = 0

∴ x = 4,−2 are the points of intersection.

Area of the region bounded by the curve y=f(x), the x-axis and the ordinates x=a and x=b, where f(x) is a continuous function defined on [a,b], is given by .

Required Area =

= 12 + 24 − 3 − (−12) − (16 − (−2))

= 27 sq. units