Definite Integration
Integration by Substitution
Grade 12
Question:
<p>The value of the integral <span>\(\int_1^e \frac{\log_e x}{x} dx\)</span> is</p>
<p>(A) \(\pi/2\)</p>
<p>(B) \(-2\)</p>
<p>(C) \(1/2\)</p>
<p>(D) \(-1/2\)</p>
Step-by-Step Solution
Key Concept: Use the substitution $u = \log_e x$ to transform this into a standard polynomial integral.
<p><strong>IIT - 2000</strong></p>
Correct Answer: C