QJEEM20Ma3c7f: JEE Main 2020 Mathematics - Class 12 JEEM20Ma3c7f Solution: The area (in sq. units) of the region { (x, y) : 0 y x 2 + 1, 0 …

Question

Verified Solution • 2025–26 Session moderate

The area (in sq. units) of the region

{ (x, y) : 0

\le

y

\le

x² + 1, 0

\le

y

\le

x + 1,

{1 \over 2}

\le

x

\le

2 } is :

Accepted Answer

A = \int\limits_{{1 \over 2}}^1 {({x^2} + 1)dx + }

\int\limits_1^2 {}

{(x + 1)dx}

=

{\left[ {{{{x^3}} \over 3} + x} \right]_{{1 \over 2}}^1 + \left[ {{{{x^2}} \over 2} + x} \right]_1^2}

{ = \left( {{4 \over 3} - {{13} \over {24}}} \right) + \left( {4 - {3 \over 2}} \right)}

{ = {{19} \over {24}} + {5 \over 2}}

{ = {{79} \over {24}}}

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