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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals2 Marks
Question
Integrate the function: $\sqrt{\sin 2 x} \cos 2 x$
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Answer

Let sin2x = t
$\Rightarrow$ 2cos2xdx = dt
$=\int \sqrt{\sin 2 x} \cos 2 x d x=\frac{1}{2} \int \sqrt{t} d t$
$\Rightarrow \frac{1}{2}\left(\frac{t^{\frac{3}{2}}}{\frac{3}{2}}\right)+C$
$\Rightarrow \frac{1}{3}(\sin 2 x)^{\frac{3}{2}}+C$

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