If _0^a[f(x)+f(-x)] ,dx= _ -a ^ag(x) ,dx then what is g(x) equal to?

NDA 2021 Mathematics question

[f(x)+f(-x)] dx=g(x) dx

then what is equal to?

Answer: (A)

Split \int_{-a}^af(x)dx=\int_{-a}^0f(x)dx+\int_0^af(x)dx. In the first integral put , : . Therefore

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Question ID VK-033571