QJEEM20Maa3ee: JEE Main 2020 Mathematics - Class 12 JEEM20Maa3ee Solution: The area (in sq. units) of the region {(x,y) ∈ R 2 : x 2 ≤ y ≤…

Question

Verified Solution • 2025–26 Session moderate

The area (in sq. units) of the region

{(x,y)

\in

R² : x²

\leq

y

\leq

3 – 2x}, is :

Accepted Answer

x²

\leq

y

\leq

– 2x + 3

\Rightarrow

x² = – 2x + 3

\Rightarrow

x² + 2x – 3 = 0

\Rightarrow

(x + 3) (x – 1) = 0

\Rightarrow

x = – 3, x = 1

Area =

\int_{- 3}^{1} (- 2 x + 3 - x^{2}) d x

=

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

=

(- 1 + 3 - \frac{1}{3} + 9 + 9 - 9)

= 11 -

\frac{1}{3}

=

\frac{32}{3}

sq. unit

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