Question

Solve ${\int }_0^{100}{e}^{x-\left[x\right]}dx=?$ where $\left[x\right]$ is greatest integer function.

• A. $100e$
• B. $100(e-1)$
• C. $100(e+1)$
• D. $100(1-e)$

Answer 1

The correct option is B $100(e-1)$

Consider, $I={\int }_0^{100}{e}^{x-\left[x\right]}dx$

$I=100{\int }_0^1{e}^{x}dx$

$I=100(e^x{)}_0^1$

$I=100(e^1-e^0)$

$I=100(e-1)$