Which of the following regions will represent the shaded area in the…

from the given figure

equation of parabola is

$y = x^2 + 2$

of straight line passing (0, 2) and (2, 6)

$\frac{y-2}{x-0} = \frac{6-2}{2-0}$

so y = 2x + 2

⇒  0 ≤ x ≤ 2

$0 ≤ y ≤ x^2+2$  (under the parabola)

and $0 ≤ y ≤ 2x+2$

⇒ Region → $\left\{(x, y): 0 ≤ y ≤ x^2+2,0 ≤ y ≤ 2 x+2,0 ≤ x ≤ 3\right\}$