Let $h: \mathbb{R} \to S^1$ be $h(t) = (\cos t, \sin t)$. How do I show that if $\omega$ is any $1$-form on $S^1$, then$$\int_{S^1} \omega = \int_0^{2\pi} h^*\omega?$$
2026-04-25 23:36:56.1777160216
$\omega$ is $1$-form on $S^1$.
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This is how the integral of a $1$-form is defined. One then checks it is independent of the parametrization used.