$\mathop \smallint \nolimits_0^{1000} \,\,{e^{x - \left[ x \right]}}\,\,dx\,\,\;{\rm{is}}$

$\frac{{{e^{1000}}\,\, - \,\,1}}{{e\,\, - \,\,1}}$

$\frac{{e\,\, - \,\,1}}{{1000}}$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \nolimits_0^{1000} \,\,{e^{x - \left[ x \right]}}\,\,dx\,\,\;\mathrm{is}

View answer and explanation

Correct option: C

1000\,\,\left( {e\,\, - \,\,1} \right)

Option C is correct because the integral is evaluated using the periodic property of the function.

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