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Question

Find the area of the region bounded by the parabola y = x2 and

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Solution

The area bounded by the parabola, x2 = y,and the line,, can be represented as

The given area is symmetrical about y-axis.

∴ Area OACO = Area ODBO

The point of intersection of parabola, x2 = y, and line, y = x, is A (1, 1).

Area of OACO = Area ΔOAB – Area OBACO

⇒ Area of OACO = Area of ΔOAB – Area of OBACO

Therefore, required area = units


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