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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
Question
Evaluate $\int \sqrt{1-\sin 2 x} d x$ :
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Answer

$\int \sqrt{1-\sin 2 x} d x$
$=\int \sqrt{\sin ^2 x+\cos ^2 x-2 \sin x \cos x} d x$
$=\int \sqrt{(\sin x-\cos x)^2} d x$
$=\int(\sin x-\cos x) d x=\int \sin x d x-\int \cos x d x$
$=-\cos x-\sin x+C$

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