# Sine - Future and Past

Calculus Level pending

If the integral $$\displaystyle I = \int \limits_0^{\pi /12084} \sin (2015 x) \sin ^{2013} x \text{ d}x$$ can be expressed as $$\displaystyle \frac{1}{c} . \bigg( \frac{\pi }{a} \bigg)^b$$ , where $$a,b$$ and $$c$$ are natural numbers.

Evaluate: $$\displaystyle \frac{ac}{b^2}$$

Details and Assumptions:

• $$\displaystyle \sin x = x$$ for small $$x$$.
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