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Find the area of the region bounded by t...

Find the area of the region bounded by the curves `y=f(x), y=|g(x)|` and lines `x = 0, x = 2`, where `f` and `g` are continuous functions satisfying `f(x+y)=f(x)+f(y)-8xy` for all `x,y in R` and `g(x+y)=g(x)+g(y)+3xy(x+y)` for all `x,y in R`. Also `f\'(0) = 8` and g\'(0)=-4`.

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