JEE Mains · Maths · STD 12 - 7.2 definite integral
If \(\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \sqrt{1-\sin 2 x} d x=\alpha+\beta \sqrt{2}+\gamma \sqrt{3}\), where \(\alpha, \beta\) and \(\gamma\) are rational numbers, then \(3 \alpha+4 \beta-\gamma\) is equal to ...........
- A \(7\)
- B \(4\)
- C \(5\)
- D \(6\)
Answer & Solution
Correct Answer
(D) \(6\)
Step-by-step Solution
Detailed explanation
\( =\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \sqrt{1-\sin 2 x} d x \) \( =\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}|\sin x-\cos x| d x \) \( =\int_{\frac{\pi}{6}}^{\frac{\pi}{4}}(\cos x-\sin x) d x+\int_{\frac{\pi}{4}}^{\frac{\pi}{3}}(\sin x-\cos x) d x \) \( =-1+2 \sqrt{2}-\sqrt{3} \)…
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