Prove that the work

produced along a oriented curve of depends **only** on the distances of starting and ending point of about the origin.

**Solution**

which is continuously differentiable in and it holds that:

Hence the vector field is a conservative one. This , in return, means that is actually independent of the road we choose , meaning that it only depends on distances of starting and ending point of about the origin.

This was an exam’s question somewhere in Greece. The answer to this question was migrated from the Greek team of mathimatikoi.org forum.