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Definite Integrals & Area · Question 24 of 71

Question 24

MediumOriginal question

Evaluate ∫1elog⁡x dx\int_1^e \log x\,dx.

Options for question 24

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. By parts, ∫log⁡x dx=xlog⁡x−x\int \log x\,dx = x\log x - x.

  2. [xlog⁡x−x]1e=(e−e)−(0−1)=1[x\log x - x]_1^e = (e - e) - (0 - 1) = 1.

Worth noting

e−1e - 1 integrates log⁡x\log x as if it were exe^{x} or forgets the −x-x.

Concept
A definite integral by parts
Typical time
90 s
Your time
—
The rule this testsSubstitution and by parts with limits
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