# Arc Length In A Rectilinear Metric?

**Calculus**Level 4

The *Minkowski plane* is defined by a rectilinear metric as follows:

For points \((a, b)\) and \((m, n)\), the distance between these points is

\[d((a,b);(m,n))=|m-a|+|n-b|\]

What is the length of the arc of \(f(x)=x^2\) from \(x=-1\) to \(x=1\) in this metric?

\[\] **Notation**: \( | \cdot | \) denotes the absolute value function.