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

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Given, equation of parabola x2 = and line + 2

Solving the above equations, we get

x2 = x + 2

x2 – x – 2 = 0

x2 – 2x + x – 2 = 0

x(x – 2) + 1(x – 2) = 0

(x + 1) (x – 2) = 0

So, x = -1, 2

Now,

Therefore, the area of the required region is 9/2 sq. units.

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