That's a great mapping

Calculus Level 4

Define a function \(f(x)\) such that \(f(x)=x^{2}\) for \(x \in [-1,1]\) and \(f(x)=f(\frac{1}{x})\) for all non-zero \(x\).

Find \(\displaystyle \int_{-\infty}^{\infty} f(x)\, dx\).


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