CUET · MATHS · PYQ PAPER 2025
\(\int_0^{\frac{\pi}{2}} \sqrt{1-\sin 2 x} d x\) is equal to :
- A \(2(\sqrt{2}-1)\)
- B \(2(\sqrt{2}+1)\)
- C 2
- D \(2 \sqrt{2}\)
Answer & Solution
Correct Answer
(A) \(2(\sqrt{2}-1)\)
Step-by-step Solution
Detailed explanation
\(\int_0^{\frac{\pi}{2}} \sqrt{1-\sin 2 x} d x = \int_0^{\frac{\pi}{2}} \sqrt{\cos^2 x + \sin^2 x - 2\sin x \cos x} d x\) \(= \int_0^{\frac{\pi}{2}} \sqrt{(\cos x - \sin x)^2} d x = \int_0^{\frac{\pi}{2}} |\cos x - \sin x| d x\)…
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