The area bounded by the curve y 2 = 1 - x and the lines y = x x , x = - 1 and x = 1 2 is

Step-by-step solution

From the diagram, the area of the shaded region, A = ∫ - 1 0 - 1 - - 1 - x d x + ∫ 0 1 2 1 - 1 - x d x = - x - 1 - x 3 2 3 2 - 1 0 + x + 1 - x 3 2 3 2 0 1 2 = - 2 3 - 1 - 2 × 2 3 2 3 + 1 2 + 2 3 × 2 3 2 - 2 3 = 2 3 × 2 3 2 + 2 × 2 3 2 3 - 4 3 - 1 2 = 3 2 - 4 3 - 1 2 = 3 2 - 11 6 s q . u n i t s