The correct option is A 83 Consider ∫_0^2x|x|dx Since 0≤ x≤ 2 we get x gt;0 ⇒∫_0^2x|x|dx=∫_0^2x^2 dx =[x^33]_0^2 ∴∫_0^2x| ...

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Rationalization Method to Remove Indeterminate Form

Solve: ∫02 x...

Question

Solve:
$2 \int 0 x | x | d x$

\frac{1}{2}

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\frac{3}{2}

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\frac{5}{2}

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\frac{8}{3}

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Solution

The correct option is A $\frac{8}{3}$
Consider $\int_{0}^{2} x | x | d x$

Since $0 \leq x \leq 2$ we get $x > 0$

$\Rightarrow \int_{0}^{2} x | x | d x = \int_{0}^{2} x^{2} d x$

$= {[\frac{x^{3}}{3}]}_{0}^{2}$

$∴ \int_{0}^{2} x | x | d x$ $= \frac{8}{3}$

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