Evaluate the following integrals: ^ 2 _1 _e[x]dx - Vidyadip

Question

Evaluate the following integrals:
$\int\limits^{2}_1\log_\text{e}[\text{x}]\text{dx}$

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Answer

We have,
$\text{I}=\int\limits^{2}_1\log_\text{e}[\text{x}]\text{dx}$
We know that,
$[\text{x}]=1,\text{ when }1<\text{x}<2$
$\therefore\ \text{I}=\int\limits^{2}_1\log_\text{e}[\text{x}]\text{dx}$
$\text{I}=\int\limits^{2}_1(0)\text{dx}$
$\text{I}=0$

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