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Q27  Integrate the functions \sqrt { \sin 2x } \cos 2x

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Given function  \sqrt { \sin 2x } \cos 2x,

Assume the \sin 2x = t

 \therefore 2\cos 2x dx =dt

\implies \int \sqrt{\sin 2x }\cos 2x dx = \frac{1}{2}\int \sqrt t dt

= \frac{1}{2}\left ( \frac{t^{\frac{3}{2}}}{\frac{3}{2}} \right )+C

= \frac{1}{3}t^{\frac{3}{2}}+C

Now, back substituted the value of t.

= \frac{1}{3}(\sin 2 x)^{\frac{3}{2}}+C , where C is any constant value.

Posted by

Divya Prakash Singh

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