QJEEM19Ma6666: JEE Main 2019 Mathematics - Class 12 JEEM19Ma6666 Solution: The area (in sq. units) of the region A = {(x, y) : x 2 y x +…

Question

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The area (in sq. units) of the region

A = {(x, y) : x²

\le

y

\le

x + 2} is

Accepted Answer

Parabola : x² = y

Straight line : y = x + 2

\therefore

x² = x + 2

\Rightarrow

x² - x - 2 = 0

x = -1, 2

\therefore

y = 1, 4

Required area =

\int\limits_{ - 1}^2 {\left[ {\left( {x + 2} \right) - {x^2}} \right]} dx

=

\left[ {{{{x^2}} \over 2} + 2x - {{{x^3}} \over 3}} \right]_{ - 1}^2

=

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

=

{{9 \over 2}}

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