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Question

Let gi:[π8,3π8]R,i=1,2 and f:[π8,3π8]R be functions such that g1(x)=1,g2(x)=|4xπ| and f(x)=sin2x, for all x[π8,3π8].
Define Si=3π8π8f(x)gi(x)dx, i=1,2

The value of 16S1π is

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