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E ∫ 1 Log X D X =(A) 1 (B) E − 1 (C) E + 1 (D) 0

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Question

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

Options

1
e − 1
e + 1
0

MCQ

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Solution

1

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

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Definite Integrals

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Chapter 19: Definite Integrals - MCQ [Page 118]

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R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12

Chapter 19 Definite Integrals
MCQ | Q 14 | Page 118

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