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Which of the following regions will represent the shaded area in the given figure?
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$\left\{(x, y): 0 ≤ y ≤ x^2+2,0 ≤ y ≤ 2 x+2,0 ≤ x ≤ 3\right\}$ $\left\{(x, y): 0 ≤ y ≤ x^2+2, y ≥ 2 x+2, x ≤ 3\right\}$ $\left\{(x, y): y ≥ x^2+2, x ≤ 2, x ≥ 0\right\}$ $\left\{(x, y): y ≥ x^2+2, x ≥ 0, x ≥ 3\right\}$ |
$\left\{(x, y): 0 ≤ y ≤ x^2+2,0 ≤ y ≤ 2 x+2,0 ≤ x ≤ 3\right\}$ |
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 → $\left\{(x, y): 0 ≤ y ≤ x^2+2,0 ≤ y ≤ 2 x+2,0 ≤ x ≤ 3\right\}$ |
