Let f(x) be a function such that f' ( 1 x )+x^3f'(x)=0. What is _ -1 ^ 1 f(x) ,dx equal to?

NDA 2016 Mathematics question

Let be a function such that . What is equal to?

Answer: (B)

Putting gives , and the relation is unchanged when is replaced by , so it is symmetric in and . The intended reading is

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Question ID VK-028542