^e_1 dx= - Vidyadip

MCQ

$\int\limits^\text{e}_1\log\text{x}\text{ dx}=$

✓
$1$
B
$e - 1$
C
$e + 1$
D
$0$

✓

Answer

Correct option: A.

$1$

$\int\limits^\text{e}_1\log\text{x}\text{ dx}$
$=\int\limits^\text{e}_1\log\text{x}\text{ x}^0\text{dx}$
$=\big[\text{x}\log\text{x}\big]^\text{e}_1-\int\limits^\text{e}_1\frac{1}{\text{x}}\text{dx}$
$=\big[\text{x}\log\text{x}\big]^\text{e}_1-\big[\text{x}\big]^\text{e}_1$
$=(\text{e}-0)-(\text{e}-1)$
$= \text{e}-\text{e}+1$
$=1$

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