JEE Mains · Maths · STD 12 - 7.2 definite integral
The integral \(\int_{1 / 4}^{3 / 4} \cos \left(2 \cot ^{-1} \sqrt{\frac{1-\mathrm{x}}{1+\mathrm{x}}}\right) \mathrm{dx}\) is equal to :
- A \(-1 / 2\)
- B \(1 / 4\)
- C \(1 / 2\)
- D \(-1 / 4\)
Answer & Solution
Correct Answer
(D) \(-1 / 4\)
Step-by-step Solution
Detailed explanation
\( I=\int_{1 / 4}^{3 / 4} \cos \left(2 \cot ^{-1}\left(\sqrt{\frac{1-x}{1+x}}\right) d x\right) \) \( \int_{1 / 4}^{3 / 4} \cos \left(2\left(\tan ^{-1} \sqrt{\frac{1+\mathrm{x}}{1+\mathrm{x}}}\right)\right) \mathrm{dx} \)…
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