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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Q)

Integrate: $\int \limits_{-1}^1 x |x| dx.$

\[\begin {array} {1 1} (a)\;2 \\ (b)\;1 \\ (c)\;0 \\ (d)\;None \end {array}\]

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A)
$-x \qquad x < 0 \qquad x=0$
$+x \qquad x >0 \qquad x=0$
$\int \limits_{-1}^0 (-x^2)dx +\int \limits_0^{1} x^2 dx$
=> $ -\bigg[ \large\frac{x^3}{3}\bigg] +\bigg[ \large\frac{x^3}{3} \bigg]_0^1$
=> $-\bigg[0-\large\frac{(-1)^3}{3} \bigg] +\bigg[ \large\frac{1}{3} -0\bigg]$
=> $ \large\frac{-1}{3} +\frac{1}{3} =0$
Hence c is the correct answer.
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