Evaluate the following integrals: ^ 1 _0e^ x dx - Vidyadip

Question

Evaluate the following integrals:
$\int\limits^{1}_0\text{e}^{\{\text{x}\}}\text{dx}$

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Answer

We have,
$\text{I}=\int\limits^{1}_0\text{e}^{\{\text{x}\}}\text{dx}$
We know that,
$\{\text{x}\}=\text{x},$ When $0<\text{x}<1$
$\therefore\ \text{I}=\int\limits^{1}_0\text{e}^{\{\text{x}\}}\text{dx}$
$=\big[\text{e}^{\text{x}}\big]^1_0$
$=\text{e}^1-\text{e}^0$
$=\text{e}-1$

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