Find the value of _ -4 ^4|x| d x. - Vidyadip

Question

Find the value of $\int_{-4}^4|x| d x$.

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Answer

Let $ I =\int_{-4}^4|x| d x=\int_{-4}^0|x| d x+\int_0^4|x| d x$
$\because \because|x|=\left\{ x, x > 0 -x, x < 0 \right.$
$\therefore =\int_{-4}^0-x d x+\int_0^4 x d x$
$ =\left(\frac{-x^2}{2}\right)_{-4}^0+\left(\frac{x^2}{2}\right)_0^4$
$ =\frac{-1}{2}(0-16)+\frac{1}{2}(16-0)=8+8=16 \text {}$

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