Rudin W. Principles of Mathematical Analysis page 256

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https://notendur.hi.is/vae11/%C3%9Eekking/principles_of_mathematical_analysis_walter_rudin.pdf

(37) $\ \int_{\phi} cw =c\int_{\phi} w$

He says by (37),

(39)$\ \int_{\phi} (-w) =-\int_{\phi} dw$

How does property (39) Come about in page 256? I don't think he even defined the differential of a differential form.

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Looks to me like a typo; should be $\int_{\phi}(-w)=-\int_{\phi}w$.

Answer by kimchi lover