Question

The value of${\int }_0^4|x-1|dx$ is

• A. $\frac{5}{2}$
• B. $5$
• C. $4$
• D. $1$

Answer 1

The correct option is B

$5$

Explanation for the correct answer.

Evaluate the integral.

$\begin{array}{rcl}{\int }_0^4|x-1|dx& =& {\int }_0^1\left(1-x\right)dx+{\int }_1^4\left(x-1\right)dx\\ & =& {\left[x-\frac{x^2}{2}\right]}_0^1+{\left[\frac{x^2}{2}-x\right]}_1^4\\ & =& \left(1-\frac{1}{2}\right)-0+\left[\left(8-4\right)-\left(\frac{1}{2}-1\right)\right]\\ & =& \frac{1}{2}+5-\frac{1}{2}\\ & =& 5\end{array}$

Hence, $o\mathrm{ption}\left(\mathrm{B}\right)$ is the correct answer.