# Differential 1 form on line

1. Homework Statement
This problem is from V.I Arnold's book Mathematics of Classical Mechanics.
Q) Show that every differential 1-form on line is differential of some function

2. Homework Equations
The differential of any function is
$$df_{x}(\psi): TM_{x} \rightarrow R$$
3. The Attempt at a Solution

The tangent to line is line itself. The differential 1-form is $dy-dx=0$. Here I am struct. I don't know how to find out the differential. Can anyone help?

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Orodruin
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The tangent to line is line itself.
No.

The differential 1-form is dy−dx=0dy−dx=0dy-dx=0.
No. A general differential 1-form is of the form $\omega = g(x) dx$. You have to show that there exists a function $G(x)$ such that $\omega = dG$.

No.

No. A general differential 1-form is of the form $\omega = g(x) dx$. You have to show that there exists a function $G(x)$ such that $\omega = dG$.
That means I have to integrate. Can you provide me solution?

Orodruin
Staff Emeritus