For example, can you integrate a 2-form on some curve, a 1-dimensional manifold, or some 3-dimensional manifold?
I know that Stokes's Theorem states that if you integrate $\omega \in \mathcal A^{k-1}(M)$ or a (k-1)-differential form when integrated over the (k-1)-dimensional boundary of the k-dimensional manifold $M$, it is equal to integrating $d\omega \in \mathcal A^{k}(M)$ over the k-dimensional manifold $M$.
I.e. $\int_{\partial M} \omega = \int_{M} d\omega$.
I'm not very confident in all this because I'm new to learning university math, I am a novice in it and I'm doing this for fun as I am in Grade 11 still so I am not really forcing myself to learn all the details which can be bad. If you can recommend an article or book that explains my question that is suitable for my level, I would appreciate it a lot. I'm studying from Professor Shifrin's lectures on Multivariable Calculus. I was recently on one of his lectures on Stoke's Theorem and it was interesting because it seemed that all the dimensions of the forms and the manifolds (or its boundaries) matched up. Therefore, I was curious if I can integrate k-forms on manifolds of dimension less than k or bigger than k, as I can integrate at least some k-forms on k-dimensional manifolds according to Stokes's Theorem.
I have edited this question as I had no details whatsoever which can seem rude so I tried to put some context into it but I'm new to this site so please bear with me.