How to determine an integral of a differential form?

145 Views Asked by At

Let $$ \eta = x^2 \, dy \wedge dz + yx\,dz \wedge dx + z^3 \, dx \wedge dy $$

Can you show me how to calculate :

$$ \int_{\Phi} \eta, $$ where $ \Phi $ is supposed to be the parametrization of the unitsphere in $\mathbb{R}^3? $

Any help very appreciated !!