QJEEM20Mad58a: JEE Main 2020 Mathematics - Class 12 JEEM20Mad58a Solution: The area (in sq. units) of the region {(x, y) ∈ R 2

Question

Verified Solution • 2025–26 Session moderate

The area (in sq. units) of the region
{(x, y)

\in

R² | 4x²

\leq

y

\leq

8x + 12} is :

Accepted Answer

For point of intersection 4x² = 8x + 12

\Rightarrow

x² - 2x - 3 = 0

\Rightarrow

x = –1, 3

Required area = area of the shaded region

=

\int_{- 1}^{3} (8 x + 12 - 4 x^{2}) d x

=

4 {[2. \frac{x^{2}}{2} + 3 x - \frac{x^{3}}{3}]}_{- 1}^{3}

= (36 + 36 – 36) – (4 – 12 +

\frac{4}{3}

)

=

\frac{128}{3}

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