I'm self-learning differential forms. I've been happily integrating 1-forms over parameterised curves, and 2-forms over parameterised surfaces, both in $\mathbb{R}^{3}$. Now I've just found out that integrating an n-form $\omega=f\left(x_{1},\ldots,x_{n}\right)dx_{1}\wedge dx_{2}\cdots\wedge dx_{n}$ over an n-dimensional manifold M in $\mathbb{R}^{n}$ is defined by$$\intop_{M}\omega=\pm\intop_{M}f\left(x_{1},\ldots,x_{n}\right)dx_{1}\cdots dx_{n}.$$
Am I correct in thinking that this definition describes what's going on with an ordinary calculus definite integral$$\int_{b}^{a}f\left(x\right)dx.$$So $f\left(x\right)dx$ would be a 1-form and the one-dimensional manifold it is integrated over is the interval $\left(a,b\right)$?