Area bounded by $y^{2} = x, y = 0, x = 1, x = 4$ is

$\frac{14}{3}$ sq units

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$\frac{3}{28}$ sq units

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$\frac{8}{3}$ sq units

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$\frac{4}{3}$ sq units

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Solution

The correct option is A
$\frac{14}{3}$ sq units

Explanation for the correct option:
Draw the graph according to the question:
where $y^{2} = x, y = 0, x = 1, x = 4$
From the figure, we have
Area bounded by the curves $=$ Area of $A B C D$
$= \int_{1}^{4} y d x = \int_{1}^{4} \sqrt{x} d x = \frac{2}{3} [{(4)}^{\frac{3}{2}} - {(1)}^{\frac{3}{2}}] = \frac{2}{3} (8 - 1) = \frac{14}{3}$
$∴$ Area bounded by the curves is $\frac{14}{3}$ sq units
Hence, Option ‘A’ is Correct.

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List-I	List-II
1. Area bounded by $y = \| x \|$ and $y = 2$ is	a. 4
2. Area bounded by $\frac{\| x \|}{a} + \frac{\| y \|}{b} = 1$ , when $a, b > 0$ is	b. $\frac{(π - 2) a b}{4}$
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