The area bounded by the curve x+y=1 and the coordinate axes is_________ sq.units

Area=4∫011-x2dx=4∫011+x-2xdx=4x+x22-43x3/201=41+12-43=6-163=23

The area bounded by the curve x+y=1 and the coordinate axes is_________ sq.units

Area=4∫011-x2dx=4∫011+x-2xdx=4x+x22-43x3/201=41+12-43=6-163=23

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The area bounded by the curve $\sqrt{|x|} + \sqrt{|y|} = 1$ and the coordinate axes is_________ sq.units

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$\frac{1}{6}$

$\frac{2}{3}$

$\frac{1}{2}$

$\frac{1}{3}$

answer is A.

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Area= $4 \int_{0}^{1} {(1 - \sqrt{x})}^{2} d x$

$= 4 \int_{0}^{1} (1 + x - 2 \sqrt{x}) d x = 4 {(x + \frac{x^{2}}{2} - \frac{4}{3} x^{3 / 2})}_{0}^{1} = 4 (1 + \frac{1}{2} - \frac{4}{3}) = 6 - \frac{16}{3} = \frac{2}{3}$

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The area bounded by the curve $\sqrt{|x|} + \sqrt{|y|} = 1$ and the coordinate axes is_________ sq.units