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

Question

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

✓

Answer

Let $\quad I =\int_{-4}^4|x| d x=\int_{-4}^0|x| d x+\int_0^4|x| d x$
$
\begin{aligned}
\because \quad & \because|x|=\left\{\begin{array}{l}
x, x>0 \\
-x, x<0
\end{array}\right. \\
\therefore \quad & =\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 {}
\end{aligned}
$

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