# integration of forms

1. ### Integral of a differential form

1. Homework Statement Suppose that a smooth differential $n-1$-form $\omega$ on $\mathbb{R}^n$ is $0$ outside of a ball of radius $R$. Show that $$\int_{\mathbb{R}^n} d\omega = 0.$$ 2. Homework Equations $$\oint_{\partial K} \omega = \int_K d\omega$$ 3. The Attempt at a...
2. ### A Exterior forms in wiki page

Hello there, I had some questions regarding k-forms. I was looking in the wiki page of differential forms(https://en.wikipedia.org/wiki/Differential_form) and noticed that it was was introduced to perform integration independent of the co-ordinates. I am not clear how? Is this because given a...