Question

Find the area of the region bounded by y = x^2 + 2x -6 and y = 3x.

Answer 1

always make a sketch of the region. The curves intersect at (-2,-6) and (3,9). Since the line lies above the parabola, the area is just
∫[-2,3] (3x - (x^2+2x-6)) dx = ∫[-2,3] (-x^2+x+6) dx = 125/6