AP EAMCET · Maths · Definite Integration
\(\int_{e^{-1}}^{e^2}\left|\frac{\log x}{x}\right| d x=\)
- A \(\frac{2}{5}\)
- B 2
- C 5
- D \(\frac{5}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{5}{2}\)
Step-by-step Solution
Detailed explanation
\(I=\int_{e^{-1}}^{e^2}\left|\frac{\log x}{x}\right| d x=\int_{e^{-1}}^1\left(-\frac{\log x}{x}\right) d x+\int_1^{e^2}\left(\frac{\log x}{x}\right) d x\) On putting \(\log x=t \Rightarrow \frac{d x}{x}=d t\)…
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