That's Pretty Long!

Calculus Level 5

\[\begin{cases} x=0 \\ \large x.e^{3y} = \sin(\pi y) \end{cases}\]

Let for \(j = 0,1,2 ,\ldots, n\). And let \(S_j\) be the area of the region bounded by the above curves and \( j \leq y \leq (j+1)\). Find \[ \large \left | \ln \left (\frac{S_{2016}}{S_{2015}} \right) \right | .\]

Notation: \( | \cdot | \) denotes the absolute value function.

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