If n is an integer,the domain of the function | vedclass

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(B) For the function $f(x) = \sqrt{\sin 2x}$ to be defined,the expression under the square root must be non-negative: $\sin 2x \geq 0$. The sine funct

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$[n\pi, n\pi + \frac{\pi}{2}]$

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(B) For the function $f(x) = \sqrt{\sin 2x}$ to be defined,the expression under the square root must be non-negative: $\sin 2x \geq 0$. The sine function is non-negative in the first and second quadrants,i.e.,in the intervals $[2n\pi, 2n\pi + \pi]$. Therefore,$2n\pi \leq 2x \leq 2n\pi + \pi$. Dividing by $2$,we get $n\pi \leq x \leq n\pi + \frac{\pi}{2}$. Thus,the domain is $[n\pi, n\pi + \frac{\pi}{2}]$.

If $n$ is an integer,the domain of the function $\sqrt{\sin 2x}$ is

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