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Let gi:[pi/8,(3pi)/8] to R , i=1,2 , and...

Let `g_i:[pi/8,(3pi)/8] to R , i=1,2 , and f:[pi/8,(3pi)/8] to R` be function such that `g_1(x)=1 , g_2(x)=abs(4x-pi) and f(x)=sin^2x` for all `x in[pi/8,(3pi)/8]` Define
`S_i=int_(pi/8)^((3pi)/8) f(x).g_i(x)dx , i=1,2`
The value of `(16S_1)/pi` is

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Let g_i:[pi/8,(3pi)/8] to R , i=1,2 , and f:[pi/8,(3pi)/8] to R be function such that g_1(x)=1 , g_2(x)=abs(4x-pi) and f(x)=sin^2x for all x in[pi/8,(3pi)/8] Define S_i=int_(pi/8)^((3pi)/8) f(x).g_i(x)dx , i=1,2 The value of (48S_2)/pi is

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