Question

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

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

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

$=1000\left[e^{x}\right]_{0}^{1}=1000\left(e-1\right)$