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.
by
Sharky Kesa