Find the area of the region bounded by the two parabolas {y}={

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

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Levi Discussed

Find the area of the region bounded by the two parabolas

y = x^{2}

and

y^{2} = x

6 mins ago

Discuss this question LIVE

6 mins ago

Text solutionVerified

Solution:

y_{1} = f (x) = x^{2}

y_{2} = g (x) = x

area=

\int_{0}^{1} g (x) - f (x) d x

\int_{0}^{1} (x^{2} - x) d x

(- \frac{x ^{3}}{3} + \frac{x ^{\frac{3}{2}}}{\frac{3}{2}})_{0}^{1}

\frac{2}{3} - \frac{1}{3}

\frac{1}{3} u n i t^{2}

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Question Text	Find the area of the region bounded by the two parabolas $y = x^{2}$ and $y^{2} = x$ .
Answer Type	Text solution:1
Upvotes	150