# CoV1

From Example Problems

Find the path that minimizes the arclength of the curve between and .

The goal is to minimize arclength as goes from to . This quantity is described in this integral:

The Euler-Lagrange equation is defined as:

where is the integrand in the integral above.

Compute the derivatives for the given problem.

since is independent of .

Simplify the expression by factoring out and putting the common denominator on the bottom.

This equation will hold only if is constant so that .

In that case,

and since ,

and so that

Therefore,