(\integral\limits\_{0}^{1000} e^{x-\left\[x\right]} dx) is e... | Mathematics | SolveeIt | Solveeit

Today, August 18

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

$1000(e-1)$

Explanation

Solution

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