QJEEM21Mabe82: JEE Main 2021 Mathematics - Class 12 JEEM21Mabe82 Solution: The area of the region bounded by y x = 2 and x 2 = y is equal…

Question

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The area of the region bounded by y

-

x = 2 and x² = y is equal to :

Accepted Answer

y

-

x = 2, x² = y

Now, x² = 2 + x

\Rightarrow

x²

-

x

-

2 = 0

\Rightarrow

(x + 1)(x

-

2) = 0

Area =

\int\limits_{ - 1}^2 {(2 + x - {x^2})}

= \left| {2x + {{{x^2}} \over 2} - {{{x^3}} \over 3}} \right|_{ - 1}^2

= \left( {4 + 2 - {8 \over 3}} \right) - \left( { - 2 + {1 \over 2} + {1 \over 3}} \right)

= 6 - 3 + 2 - {1 \over 2} = {9 \over 2}

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