Definite Integration Question 70
Question: $ \int _{0}^{1000}{{e^{x-[x]}}dx} $ is
[AMU 2002]
Options:
A) $ e^{1000}-1 $
B) $ \frac{e^{1000}-1}{e-1} $
C) $ 1000(e-1) $
D) $ \frac{e-1}{1000} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ {e^{x-[x]}} $ is a periodic function with period 1.
$ \therefore \int_0^{1000}{{e^{x-[x]}}dx=1000\int_0^{1}{{e^{x-[x]}}dx}} $ , $ [\because [x]=0,if0<x<1] $
$ =1000[e^{x}]_0^{1} $
$ =1000(e-1) $ .
BETA
