AP EAMCET · Maths · Definite Integration
\(\int_{1 / 2}^{1 / \sqrt{2}} \frac{1}{\left(x+\sqrt{1-x^2}\right)\left(1-x^2\right)} d x=\)
- A \(\log (\sqrt{3}+1)\)
- B \(\log (\sqrt{3}-1)\)
- C \(\log (3+\sqrt{3})\)
- D \(\log (3-\sqrt{3})\)
Answer & Solution
Correct Answer
(D) \(\log (3-\sqrt{3})\)
Step-by-step Solution
Detailed explanation
Let \(x = \sin \theta \implies dx = \cos \theta \, d\theta\). Limits: \(x=1/2 \implies \theta=\pi/6\), \(x=1/\sqrt{2} \implies \theta=\pi/4\).…
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