The smaller area (in sq. units) included between the curves x + | y | = 1 and | x | + | y | = 1 is

Question

The smaller area (in sq. units) included between the curves $\sqrt{x} + \sqrt{| y |} = 1$ and $| x |$ $+$ $| y |$ $= 1$ is

Smart Achievers · Accepted Answer

(3)

$\sqrt{x} + \sqrt{| y |} = 1 .$

$Above curve is symmetric about x -axis$ $\sqrt{| y |} = 1 - \sqrt{x} and \sqrt{x} = 1 - \sqrt{| y |}$

$\Rightarrow x > 0, y = 0$

$\sqrt{y} = 1 - \sqrt{x}$

$\frac{1}{2 \sqrt{y}} \frac{d y}{d x} = - \frac{1}{2 \sqrt{x}}$

$\frac{d y}{d x} = - \sqrt{\frac{y}{x}} < 0$

$Function is decreasing$

$Required area = 2 \int_{0}^{1} (2 \sqrt{x} - 2 x) d x = \frac{2}{3}$

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