Question

Find the area of the region enclosed by the parabola x² = y, the line y = x + 2 and x-axis

Answer 1

The area of the region enclosed by the parabola, x² = y, the line, y = x + 2, and x-axis is represented by the shaded region OACO as

The point of intersection of the parabola, x² = y, and the line, y = x + 2, is A (–1, 1) and C(2, 4).

     Area of OACO = ∫-12x + 2 dx  -  ∫-12 x2 dx⇒Area of OACO = x22 + 2x-12 - 13x3-12⇒Area of OACO = 222+22 - -122+2-1 - 1323 - -13⇒Area of OACO = 2 + 4 - 12-2 - 138 + 1⇒Area of OACO = 6 + 32 - 3⇒Area of OACO = 3 + 32 = 92 square units