Integration of differential forms

[Trenters4325]

When you integrate differential forms, how can you just take out the wedge product?

 

[ChaoticLlama]

When you integrate differential forms, how can you just take out the wedge product?

Pardon? I have no idea what you are asking. Lessons are not taught here, please post a specific problem that you have.

 

[Trenters4325]

Take the 1-form \(\displaystyle \omega = - ydx + x^2 dy\) for example. We want to integrate \(\displaystyle d\omega\) on the sector S of a circle with radius 8 from 0 to pi/4.

We take the exterior derivative of omega:

\(\displaystyle d\omega = \left( {2x + 2y} \right)dx \wedge dy\)

Now we have:

\(\displaystyle \int\limits_S {\left( {2x + 2y} \right)dx \wedge dy}\)

How do I complete the problem and how do I get rid of the wedge product?