# 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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