# 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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