The area (in square units) bounded by y = x 2 + x + 1 and x + y = 2 is

Step-by-step solution

Area = ∫ x 1 x 2 2 - x - x 2 + x + 1 d x where x 1 and x 2 are roots of the equation 2 - x = x 2 + x + 1 ⇒ x 2 + 2 x - 1 = 0 So, x 1 + x 2 = - 2 ,   x 1 x 2 = - 1 ,   x 1 - x 2 = 4 + 4 = 2 2 Hence, the required area = ∫ x 1 x 2 1 - 2 x - x 2 d x = x 2 - x 1 1 - x 2 + x 1 - x 2 2 + x 2 x 1 + x 1 2 3 = 2 2 1 - - 2 - 4 - - 1 3 = 2 2 3 - 5 3 = 8 2 3 sq. units