JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of the integral \(\int\limits_0^1 {x\,{{\cot }^{ - 1}}\,\left( {1 - {x^2} + {x^4}} \right)} dx\) is
- A \(\frac{\pi }{4} - \frac{1}{2}\,{\log _e}\,2\)
- B \(\frac{\pi }{2} - {\log _e}\,2\)
- C \(\frac{\pi }{2} - \frac{1}{2}\,{\log _e}\,2\)
- D \(\frac{\pi }{4} - {\log _e}\,2\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi }{4} - \frac{1}{2}\,{\log _e}\,2\)
Step-by-step Solution
Detailed explanation
\(\mathrm{I}=\int_{0}^{1} \mathrm{x} \cot ^{-1}\left(1-\mathrm{x}^{2}+\mathrm{x}^{4}\right) \mathrm{d} \mathrm{x}\) \(I=\int_{0}^{1} x \tan ^{-1}\left(\frac{1}{1-x^{2}+x^{4}}\right) d x\)…
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