Let gi:[π8,3π8]→R,i=1,2 and f:[π8,3π8]→R be functions such tha – InterviewSolution

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1.	Let gi:[π8,3π8]→R,i=1,2 and f:[π8,3π8]→R be functions such that g1(x)=1,g2(x)=\|4x−π\| and f(x)=sin2x, for all x∈[π8,3π8].If Si=3π/8∫π/8f(x)⋅gi(x)dx,i=1,2, then the value of 48S2π2 is
Answer» Let $g_{i} : [\frac{π}{8}, \frac{3 π}{8}] \to R, i = 1, 2$ and $f : [\frac{π}{8}, \frac{3 π}{8}] \to R$ be functions such that $g_{1} (x) = 1, g_{2} (x) = \| 4 x - π \|$ and $f (x) = {sin}^{2} x,$ for all $x \in [\frac{π}{8}, \frac{3 π}{8}] .$ If $S_{i} = 3 π / 8 \int π / 8 f (x) \cdot g_{i} (x) d x, i = 1, 2,$ then the value of $\frac{48 S_{2}}{π^{2}}$ is

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