Question

\[\int\limits_1^e \log x\ dx =\]

पर्याय

• 1

•  e − 1

• e + 1

•  0

Answer 1

 1

\[\int_1^e \log x d x\]
\[ = \int_1^e \log x x^0 d x\]
\[ = \left[ x \log x \right]_1^e - \int_1^e \frac{1}{x}x d x\]
\[ = \left[ x \log x \right]_1^e - \left[ x \right]_1^e \]
\[ = \left( e - 0 \right) - \left( e - 1 \right)\]
\[ = e - e + 1\]
\[ = 1\]