The area of the region enclosed by y ≤ 4 x 2, x 2 ≤ 9 y and y ≤ 4, is equal to :

Question

The area of the region enclosed by y ≤ 4 x 2, x 2 ≤ 9 y and y ≤ 4, is equal to : (A) (40/3) (B) (56/3) (C) (112/3) (D) (80/3)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/7eddb437e61c1af33874889ab36af229-.png" /> Δ=2 ⋅ ∫ limits04(3 √y-(√y/2)) d y =2 ⋅ ∫ limits04 (5/2) √y d y=(80/3)

Q. The area of the region enclosed by $y \leq 4 x^{2}, x^{2} \leq 9 y$ and $y \leq 4$ , is equal to :

$\frac{40}{3}$

$\frac{56}{3}$

$\frac{112}{3}$

$\frac{80}{3}$

$Δ = 2 \cdot 0 \int 4 (3 y - \frac{y}{2}) d y$
$= 2 \cdot 0 \int 4 \frac{5}{2} y d y = \frac{80}{3}$

Q. The area of the region enclosed by y≤4x2,x2≤9y and y≤4, is equal to :

340​

356​

3112​

380​