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Question

Question: \(\int_{0}^{1000}{e^{x–\lbrack x\rbrack}dx}\) is -...

∫01000ex–[x]dx\int_{0}^{1000}{e^{x–\lbrack x\rbrack}dx} is -

A

e1000 – 1

B

e1000–1e–1\frac{e^{1000}–1}{e–1}

C

1000 (e – 1)

D

e–11000\frac{e–1}{1000}

Answer

1000 (e – 1)

Explanation

Solution

1000∫01ex–[x]dx\int_{0}^{1}{e^{x–\lbrack x\rbrack}dx}Ž1000∫01exdx\int_{0}^{1}{e^{x}dx}Ž =1000 (e – 1)