(\integral\_{n–1}^{n}e^{x–\lbrack x\rbrack}) dx = | MATH - FUNDAMENTAL DEFINITE INTEGRATION, DEFINITE INTEGRATION BY SUBSTITUTION | SolveeIt | Solveeit

Today, August 18

Question

$\int_{n–1}^{n}e^{x–\lbrack x\rbrack}$ dx =

A

$\frac{e^{1000}–1}{1000}$

B

$\frac{e^{1000}–1}{e–1}$

C

1000 (e – 1)

D

$\frac{e–1}{1000}$

Answer

1000 (e – 1)

Explanation

Solution

$\int_{n–1}^{n}e^{\{ x\}}dx$ = n – (n – 1) $\int_{0}^{1}e^{\{ x\}}dx$

= $\int_{0}^{1}e^{x}dx$ = e –1