Question

The value of $\underset{0}{\overset{15}{\int }}\{3x+4\}dx$ is
(where $\{\cdot \}$ is fractional part function)

• A. $\frac{15}{2}$
• B. $15$
• C. $30$
• D. $5$

Answer 1

The correct option is A $\frac{15}{2}$

$\underset{0}{\overset{15}{\int }}\{3x+4\}dx=\underset{0}{\overset{15}{\int }}\left\{3x\right\}dx$
$(\because \{x+I\}=\{x\left\}\right)$
Put $3x=t\Rightarrow 3dx=dt$
$=\frac{1}{3}\underset{0}{\overset{45}{\int }}\left\{t\right\}dt=\frac{1}{3}\times 45\times \frac{1}{2}=\frac{15}{2}$