_ 0 ^ 1000 e^ x-[x] d x is equal to where [ ∙ ] denotes the greatest integer function.
Mathematics · JEE Main · NTA Exams — Integral Calculus
\(\int_{0}^{1000} e^{x-[x]} d x\) is equal to where [ ∙ ] denotes the greatest integer function.
- \(\frac{e^{100}-1}{e-1}\)
- \(\frac{e^{1000}-1}{1000}\)
- \(\frac{e-1}{1000}\)
- \(1000[e-1]\)
Answer
(A) e^ 100 -1 e-1
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