WBJEE · Maths · Definite Integration
The value of the integral \(I=\int_{1 / 2014}^{2014} \frac{\tan ^{-1} x}{x} d x\) is
- A \(\frac{\pi}{4} \log 2014\)
- B \(\frac{\pi}{2} \log 2014\)
- C \(\pi \log 2014\)
- D \(\frac{1}{2} \log 2014\)
Answer & Solution
Correct Answer
(B) \(\frac{\pi}{2} \log 2014\)
Step-by-step Solution
Detailed explanation
We have, \[ I=\int_{1 / 2014}^{2014} \frac{\tan ^{-1} x}{x} d x \] Let \[ x=\frac{1}{t} \] \(\Rightarrow\) \[ d x=\frac{-1}{t^{2}} d t \] Now,…
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