The area (in sq. units) of...|Area Under Curve|JEEMAIN 2020

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JEE MAIN 2020

08-04-20 S2

Question

The area (in sq. units) of the region $\left\{(x, y) \in \mathbb{R}^2: x^2 \leq y \leq 3-2 x\right\}$, is

Select the correct option:

$\frac{31}{3}$

$\frac{29}{3}$

$\frac{34}{3}$

$\frac{32}{3}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

x² − y ≤ 0 and 2x + y − 3 ≤ 0 For Point of intersection we have x² + 2x − 3 = 0 ⇒ x = 1, x = −3 ⇒ P(1, 1) and Q(−3, 9) are point of intersection ∴ Required area = ∫₋³¹ (3 − 2x − x²) dx = 12 − (x²)₋³¹ − 1/3 (x³)₋³¹ = 12 − (1 − 9) − 1/3 (1 + 27) = 20 − 28/3 = 11 − 1/3 = 32/3

Question Tags

JEE Main

Mathematics

Easy

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