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int(0)^((pi)/(2))sqrt(1+sin2x)...

int_(0)^((pi)/(2))sqrt(1+sin2x)

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Evaluate int_(0)^((pi)/(2))sqrt(1+sin 2x) dx .

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Show : int_(0)^((pi)/(2))sinxf(sin2x)dx=int_(0)^((pi)/(2))cosxf(sin2x)dx