The area bounded by the curve $y = x | x |$ , X-axis and the coordinates $x = - 1$ and $x = 1$ is given by

10

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\frac{1}{3}

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\frac{2}{3}

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\frac{4}{3}

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Solution

The correct option is D $\frac{2}{3}$
Given, $y = x | x | = {\begin{matrix} x^{2}, & x \geq 0 - x^{2}, & x < 0 \end{matrix}$

$∴$ Required area $= 2 \int_{0}^{1} x | x | d x = 2 \int_{0}^{1} x^{2} d x$

$= 2 {[\frac{x^{3}}{3}]}_{0}^{1} = 2 (\frac{1}{3} - 0) = \frac{2}{3}$ .

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The area bounded by the curve y=x|x|, X-axis and the coordinates x=−1 and x=1 is given by

The correct option is D 23Given, y=x|x|={x2,x≥0−x2,x<0∴ Required area =2∫10x|x|dx=2∫10x2dx=2[x33]10=2(13−0)=23.

The area bounded by the curve $y = x | x |$ , X-axis and the coordinates $x = - 1$ and $x = 1$ is given by

The correct option is D $\frac{2}{3}$
Given, $y = x | x | = {\begin{matrix} x^{2}, & x \geq 0 - x^{2}, & x < 0 \end{matrix}$

$∴$ Required area $= 2 \int_{0}^{1} x | x | d x = 2 \int_{0}^{1} x^{2} d x$

$= 2 {[\frac{x^{3}}{3}]}_{0}^{1} = 2 (\frac{1}{3} - 0) = \frac{2}{3}$ .