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.

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