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Definite Integration

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Let gi:[‌
π
8
,‌
3π
8
]→ℝ,i=1,2, and f:[‌
π
8
,‌
3π
8
]→ℝ be functions such that g1(x)=1,g2(x)=|4x−π| and f(x)=sin2x, for all x∈[‌
π
8
,‌
3π
8
]
Define Si=
∫
‌
π
8
‌
3π
8
f(x)⋅gi(x)dx,i=1,2
Section: Mathematics
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Question : 12 of 46
 
Marks: +1, -0
The value of ‌
16S1
π
 is_________
[JEE Adv 2021 P2]
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