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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