The area (in sq. units) of the region (x, y)ϵ R2|4x2 le y le 8x+12 is :

Question

The area (in sq. units) of the region (x, y)ϵ R2|4x2 le y le 8x+12 is : (A) (125/3) (B) (128/3) (C) (124/3) (D) (127/3)

Tardigrade Admin · Accepted Answer

4x2-y le 0 and 8x-y+12 ge 0 On solving y = 4x2 and y = 8x + 12 We get A (-1, 4) B(3, 36) Required area = area of the shaded region =∫ limits3-1(8x + 12 - 4x2 )dx=(128/3)

Q. The area (in sq. units) of the region ${(x, y) ϵ R^{2} ∣4 x^{2} \leq y \leq 8 x + 12}$ is :

$\frac{125}{3}$

$\frac{128}{3}$

$\frac{124}{3}$

$\frac{127}{3}$

$4 x^{2} - y \leq 0$ and $8 x - y + 12 \geq 0$
On solving $y = 4 x^{2}$
and $y = 8 x + 12$
We get $A (- 1, 4) & B (3, 36)$
Required area = area of the shaded region
$= - 1 \int 3 (8 x + 12 - 4 x^{2}) d x = \frac{128}{3}$

Q. The area (in sq. units) of the region {(x,y)ϵR2∣4x2≤y≤8x+12} is :

3125​

3128​

3124​

3127​