# Twisted minds

Calculus Level 3

Consider the function on three variables defined as $$F(x,y,z) = (xy, yz, zx)$$. Let $$C$$ be the twisted cubic polynomial curve given by $$\mathbf{r}(t) = (t,t^2,t^3)$$ as $$t$$ moves from 0 to 1. What is the value of $N = \int_C F \cdot dr ?$

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