JEE Mains · Maths · STD 12 - 7.2 definite integral
\(4 \int_0^1\left(\frac{1}{\sqrt{3+x^2}+\sqrt{1+x^2}}\right) d x-3 \log _e(\sqrt{3})\) is equal to :
- A \(2+\sqrt{2}+\log _e(1+\sqrt{2})\)
- B \(2-\sqrt{2}-\log _e(1+\sqrt{2})\)
- C \(2+\sqrt{2}-\log _e(1+\sqrt{2})\)
- D \(2-\sqrt{2}+\log _e(1+\sqrt{2})\)
Answer & Solution
Correct Answer
(B) \(2-\sqrt{2}-\log _e(1+\sqrt{2})\)
Step-by-step Solution
Detailed explanation
\(4 \int_0^1 \frac{1}{\sqrt{3+\mathrm{x}^2}+\sqrt{1+\mathrm{x}^2}} \mathrm{dx}-3 \ln \sqrt{3} \) \( =4 \int_0^1 \frac{\sqrt{3+\mathrm{x}^2}-\sqrt{1+\mathrm{x}^2}}{\left(3+\mathrm{x}^2\right)-\left(1-\mathrm{x}^2\right)} \mathrm{dx}-\frac{3}{2} \ln 3 \)…
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