If `f` is an integrable function, show that `int_(-a)^a xf(x^2)dx=0`

Explanation

We have to proof `int_(-a)^a xf(x^2)dx=0`

Now we have tp check function is even or odd

Let `g(x) = xf(x^2) `

`g(–x) = –x f((–x)^2) `

`g(–x) = – xf(x^2) `

`g(–x) = – g(x)`

Hence the function is odd.

Now as we know

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