Question

$\underset{0}{\overset{1000}{\int }}{e}^{x-\left[x\right]}dx$ is equal to

• A. $\frac{e^{1000}-1}{e-1}$
• B. $\frac{e^{1000}-1}{1000}$
• C. $\frac{e-1}{1000}$
• D. $1000(e-1)$

Answer 1

Answer: (D)

Let $I=\underset{0}{\overset{1000}{\int }}{e}^{x-\left[x\right]}dx$

We know that the period of $x-\left[x\right]$ is $1$

$\therefore I=1000\underset{0}{\overset{1}{\int }}{e}^{x}dx$

$=1000{\left[e^x\right]}_0^1=1000\left(e-1\right)$