WBJEE · Maths · Definite Integration
The value of the integral \(\int_{-1 / 2}^{1 / 2}\left\{\left(\frac{x+1}{x-1}\right)^{2}+\left(\frac{x-1}{x+1}\right)^{2}-2\right\}^{1 / 2} d x\) is equal to
- A \(\log _{e}\left(\frac{4}{3}\right)\)
- B \(4 \log _{e}\left(\frac{3}{4}\right)\)
- C \(4 \log _{e}\left(\frac{4}{3}\right)\)
- D \(\log _{e}\left(\frac{3}{4}\right)\)
Answer & Solution
Correct Answer
(C) \(4 \log _{e}\left(\frac{4}{3}\right)\)
Step-by-step Solution
Detailed explanation
\(\int_{-1 / 2}^{1 / 2} \sqrt{\left(\frac{x+1}{x-1}\right)^{2}+\left(\frac{x-1}{x+1}\right)^{2}-2} d x=\int_{-1 / 2}^{y / 2}\left|\frac{x+1}{x-1}-\frac{x-1}{x+1}\right| d x\)…
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