The integral _ -1/2 ^ 1/2 ([x]+ _e ( 1+x 1-x ) )dx, where [x] represents greatest integer function, equals

MHT CET 2024 Mathematics question

The integral , where represents greatest integer function, equals

Answer: (A)

Split the integral. The function is odd, since , so . For the greatest integer part: on , and on

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Question ID VK-093431