How do I derive the Fundamental Theorem of Calculus from the generalized Stokes theorem?
2026-03-27 03:45:13.1774583113
Deriving FTC from the generalized Stokes.
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Let $f:[a,b]\to\mathbb{R}$. Note that $[a,b]$ is a 1-dimensional manifold with boundary = $\{a,b\}$. Stokes theorem says $\int_{\partial[a,b]}f=\int_{[a,b]}df$. LHS is just $f(b)-f(a)$ (the minus sign is due to the induced orientaion), and RHs is $\int_a^bf'(x)dx$.