Sine

Calculus Level 5

If the arc length for a full period of sine function can be written as \[\Large \frac{ab\pi^b+(\Gamma(\frac{1}{a}))^a}{\sqrt{b\pi} (\Gamma(\frac{1}{a}))^b}\] for positive integers \(a\) and \(b\). Find \(a\times b\).

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