If x (2n , 2n + ) then _0^x [ x] ,dx, where [x] = greatest integer less than or equal to x, is equal to

JEE Advanced Mathematics question

If then , where = greatest integer less than or equal to , is equal to

Answer: (B)

(Here is a non-negative integer; is the variable of integration.) Split as .

*First part.* has period , so . On , with only at , so

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Question ID VK-109526