JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Application +4 | -1

The value of

\sum\limits_{{n=1}}^{1000} \int_{n-1}^n e^{x-[x]} \mathrm{d} x

is ([x] is the greatest integer function)

View answer and explanation

Correct option: C

1000(e-1)

Option C (

1000(e-1)

) is correct because the integral simplifies to a sum of identical integrals due to the periodicity of the fractional part function.

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