The value of _1^e x d x is - Vidyadip

MCQ

The value of $\int_1^e \log x d x$ is

A
$0$
B
1
C
$e$
D
$e \log e$

✓

Answer

Let $I=\int_1^e \log x d x$
Using integration by parts, we get $I=[x \log x]_1^e-\int_1^e \frac{1}{x} \cdot x d x$
$\begin{array}{l}I=[x \log x]_1^e-[x]_1^e=e \log e-\log 1-e+1 \\ =e-0-e+1=1 \quad[\because \log e=1 \text { and } \log 1=0]\end{array}$

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