JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of the integral \(\int \limits_{1 / 2}^2 \frac{\tan ^{-1} x}{x} d x\) is equal to
- A \(\pi \log _e 2\)
- B \(\frac{1}{2} \log _{ e } 2\)
- C \(\frac{\pi}{4} \log _e 2\)
- D \(\frac{\pi}{2} \log _{ e } 2\)
Answer & Solution
Correct Answer
(D) \(\frac{\pi}{2} \log _{ e } 2\)
Step-by-step Solution
Detailed explanation
\(I =\int \limits_{1 / 2}^2 \frac{\tan ^{-1} x }{ x } dx\) \(\text { Put } x \quad =\frac{1}{ t } dx =-\frac{1}{ t ^2} dt\)…
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