# Integrate the unknown function please

Calculus Level 5

Let $$g\left( x \right)$$ be a quartic ($${ 4 }^\text{th}$$ degree) polynomial such that $$g\left( n \right) ={ n }^{ 3 }-{ 2 }^{ n }$$ for $$n=0,1,2,3,4$$.

Find

$45\int _{ 0 }^{ 4 }{ g\left( x \right) dx }$

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