Question

$\underset{0}{\overset{1}{\int }}\left|5x-3\right|dx$ is equal to

• A. $\frac{10}{13}$
• B. $\frac{31}{10}$
• C. $\frac{13}{10}$
• D. None of these

Answer 1

Answer: (C)

$I={\int }_0^1|5x-3|dx$
Now, $|5x-3|=\{\begin{array}{ll}5x-3& ;x\ge \frac{3}{5}\\ -(5x-3)& ;x<\frac{3}{5}\end{array}$
$\therefore I={\int }_0^1|5x-3|dx={\int }_0^{3/5}-(5x-3)dx+{\int }_{3/5}^1(5x-3)dx$
$=-{\left[\frac{5x^2}{2}-3x\right]}_0^{1/5}+[\frac{5x^2}{2}-3x^1$
$=-\left[\left(\frac{5}{2}\times \frac{9}{25}-\frac{9}{5}\right)-(0-0)\right]+[\left(\frac{5}{2}-3\right)$
$-\left(\frac{5}{2}\times \frac{9}{25}-\frac{9}{5}\right)]$
$=-\frac{45}{50}+\frac{9}{5}-\frac{1}{2}-\frac{45}{50}+\frac{9}{5}=\frac{13}{10}$