Question

The value of integral $\underset{0}{\overset{18.7}{\int }}\left\{x\right\}dx$ is equal to
(where $\{\cdot \}$ denotes the fractional part function )

• A. $9$
• B. $9.245$
• C. $18.49$
• D. $0$

Answer 1

The correct option is B $9.245$

$\underset{0}{\overset{18.7}{\int }}\left\{x\right\}dx=\underset{0}{\overset{18}{\int }}\left\{x\right\}dx+\underset{18}{\overset{18.7}{\int }}\left\{x\right\}dx=18\underset{0}{\overset{1}{\int }}xdx+\underset{18}{\overset{18.7}{\int }}(x-18)dx=18\left(\frac{1}{2}\right)+{\frac{(x-18{)}^2}{2}|}_{18}^{18.7}=9+0.245=9.245$