The value of $\int_0^{1000}e^{x-[x]}dx$ is ([.] denotes the greatest integer function):
Answer & explanation
Correct answer: option 2
$I=\int\limits_0^{1000}e^{\{x\}}dx=1000\int\limits_0^{1}e^{\{x\}}dx=1000(e-1)$
The value of $\int_0^{1000}e^{x-[x]}dx$ is ([.] denotes the greatest integer function):
Correct answer: option 2
$I=\int\limits_0^{1000}e^{\{x\}}dx=1000\int\limits_0^{1}e^{\{x\}}dx=1000(e-1)$