Integrating is Integral

Calculus Level 4

Let \(R\) be the region bounded by the graphs of \(y=\sin{(\pi x)}\) and \(y=x^3 -4x\). The region \(R\) is the base of a solid. For this solid, each cross section perpendicular to the \(x\)-axis is a square. Find the volume of this solid to the nearest integer.

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