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If n is a positive integer, then $$\int_{0}^{\pi} \frac{sin(2nx)}{sinx} dx$$

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If n is a positive integer then just for the sake of simplicity we can assume n to be 1..

It will become sin2x/sinx..

Which is 2cosx..

After integration you will get 0..

I've checked the same for 2 as well as 3..

The answer is same which is 0..

Hope it helps!! 

Please comment if there is anything wrong!!

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