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Home  >>  CBSE XII  >>  Math  >>  Application of Integrals
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Evaluate: $\large \int \limits_{-1}^1 $$x$ $ \left | x \right |$ $ dx$.


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  • Whenever a function is represented by y=|x| two cases arises.
  • (i) y=x if $x\geq 0;$
  • (ii) y=-x if $x< 0;$
  • $\int_{-a}^{a} f(x)\:dx=0$ if $f(x)$ is odd function.
Here the given function is $y=f(x)=x|x|$
and the limits are -1 to 1.
$f(x)=x|x|$ and $f(-x)=-x|x|.$
$\therefore\: f(x)$ is an odd function
We know that $\int _{-a} ^{a} f(x)\:dx=0$ if $ f(x)$ is odd function.
$\therefore\:\int _{-1}^ {1} x|x|\:dx=0$
answered Feb 10, 2014 by rvidyagovindarajan_1
edited Feb 10, 2014 by rvidyagovindarajan_1

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