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