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Calculus Level 3

{f(1729)=4f(1730)=5f(1731)=6 \large \begin{cases} {f(1729) = 4} \\ {f(1730) = 5} \\ {f(1731)=6} \\ \end{cases}

Let f(x)f(x) be a cubic polynomial satisfying the following system of equations. Find 17291731f(x)dx\displaystyle\int _{ 1729 }^{ 1731 }{ f(x)dx } .

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