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Find the area of the region enclosed by the parabola {x}^{{{2}

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Find the area of the region enclosed by the parabola $x^{2} = y$ and the line y = x+ 2.

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Owen Discussed

Find the area of the region enclosed by the parabola

x^{2} = y

and the line y = x+ 2.

14 mins ago

Discuss this question LIVE

14 mins ago

Text solutionVerified

Solution: Area=

\int_{- 1}^{2} y d x

\int_{- 1}^{2} ((x + 2) - (x^{2})) d x

(\frac{x ^{2}}{2} + 2 x - \frac{x ^{3}}{3})_{- 1}^{2}

(\frac{1}{2} (4 - 1) + 2 (2 + 1) - \frac{1}{3} (2^{3} + 1))

\frac{3}{2} + 6 - 3

\frac{9}{2}

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Question Text	Find the area of the region enclosed by the parabola $x^{2} = y$ and the line y = x+ 2.
Answer Type	Text solution:1
Upvotes	150