MHT CET · Maths · Definite Integration
\(\int_0^1 \tan ^{-1} x d x=\)
- A \(\frac{\pi}{4}-\log 2\)
- B \(\frac{\pi}{4}-\log \sqrt{2}\)
- C \(\frac{\pi}{4}+\log 2\)
- D \(\frac{\pi}{4}+\log \sqrt{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{\pi}{4}-\log \sqrt{2}\)
Step-by-step Solution
Detailed explanation
\(\int_0^1 \tan^{-1}x dx = [x\tan^{-1}x]_0^1 - \int_0^1 \frac{x}{1+x^2}dx\) \(= [x\tan^{-1}x - \frac{1}{2}\log(1+x^2)]_0^1\)
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