Find the areas of the regions enclosed by lines and curves...?

Question

y = -x^2 - 2x and y = x

Answer 1

Intersect when -x² - 2x = x
x² + 3x = 0
x.(x + 3) = 0
x = 0, x = - 3
Points are (0,0,) and (-3,- 3)
A = ∫(-x² - 2x) - x dx between lims. -3 and 0
A = ∫-x² - 3x dx between lims. -3 and 0
A = - [x³ / 3 + 3x² / 2 ] between lims. - 3 and 0
A = - (- 27/3 + 27/2)
A = - (- 54/6 + 81/6)
A = - 27/6
A = - 9/2
A = 9/2 units² (ignoring -ve sign)