WBJEE · Maths · Definite Integration
\(\int_0^{1000} e^{x-[x]}\) is equal to
- A \(\frac{e^{1000}-1}{e-1}\)
- B \(\frac{e^{1000}-1}{1000}\)
- C \(\frac{e-1}{1000}\)
- D \(1000(\mathrm{e}-1)\)
Answer & Solution
Correct Answer
(D) \(1000(\mathrm{e}-1)\)
Step-by-step Solution
Detailed explanation
Hins : \(I=1000 \int_0^1 \mathrm{e}^{x-[x]}\) \(=1000 \int_0^1 e^x d x=1000\left(e^x\right)_0^1=100(e-1)\) Period of function is 1
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