TS EAMCET · Maths · Definite Integration
If \(f(x)=\frac{|\log x|}{x^2}\), then \(\int_{1 / e}^e f(x) d x=\)
- A \(\mathrm{e}\)
- B \(1-\frac{1}{e}\)
- C \(e^2\left(1-\frac{1}{e}\right)\)
- D \(2\left(1-\frac{1}{e}\right)\)
Answer & Solution
Correct Answer
(D) \(2\left(1-\frac{1}{e}\right)\)
Step-by-step Solution
Detailed explanation
We have, \[ f(x)=\frac{|\log x|}{x^2}= \begin{cases}\frac{-\log x}{x^2}, & 0 < x < 1 \\ \frac{\log x}{x^2}, & 1 < x < \infty\end{cases} \] Now, as \(\frac{1}{e}=0.367\) and \(e \approx 2.7182\)…
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