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 ΔOAM – Area OMACO

Area of ΔOAM $= \frac{1}{2} \times O M \times A M$

Area of OMACO

⇒ Area of OACO = Area of ΔOAM – Area of OMACO

Therefore, required area = units

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Similar questions

Find the area of the region bounded by the parabola $y = x^{2}$ and y = |x|.

y = x^{2}

y^{2} = x

y = x^{2} + 1

x + y = 3

y = x^{2}

y = x

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