Find the area of the region enclosed

Question

Y=-9x^2-48x-39 and y=-4^2-3x+1 between x=-2 and x=3

Answer 1

Intersection of curves: - 9x² - 48x - 39 = - 4x² - 3x + 1; 5x² + 45x + 40 = 0; x² + 9x + 8 = 0;

(x + 1)(x + 8) = 0; x = - 1 or x = - 8;

Area A = ∫_-2^-1(- 9x² - 48x - 39 + 4x² + 3x - 1)dx + ∫_-1³ (- 4x² -3x + 1 + 9x² + 48x + 39)dx

= ∫_-2^-1(- 5x² - 45x- 40)dx + ∫_-1³(5x² + 45x + 40)dx = (- 5x³/3 - 45x²/2 - 40x)_-2^-1 + (5x³/3 + 45x²/2 + 40x)_-1³ =

(5/3 - 45/2 + 40) - (40/3 - 90 + 80) + (45 + 405/2 + 120) - (- 5/3 + 45/2 - 40) = 402.5