Question

Solve: $\stackrel{4}{\underset{-4}{\int }}(|x-4|)dx$.

Answer 1

We have, $|x-4|=\{\begin{array}{c}x-4\text{if}x\ge 4\\ 4-x\text{if}x<4\end{array}$......(1).

Now,

$\stackrel{4}{\underset{-4}{\int }}(|x-4|)dx$

$=\stackrel{4}{\underset{-4}{\int }}(x-4)dx$ [ Using (1)]

$=0-4.8$ [ Since $x$ is an odd function]

$=-32$.