I am reading Spivak's Differential Geometry Vol. 1. I am stuck for some days in chapter 8 about integrating forms on manifolds. Maybe someone can clear my doubt.(adsbygoogle = window.adsbygoogle || []).push({});

First, I will 'type' what the corollary says:

My doubt is regarding this affirmation:

The book it says is easy to see. Well I think the (-1)^{n-1}, does not exist. I worked in the n=2 case just to see where I was doing an error, but still I have that negative sign does not exist.

I will post my working out:

http://postimg.org/image/ghfrg9jq1/

I believe Fubini is justified. A good person that was trying to help me, said that instead of Fubini, I can only interchange the integrals adding the (-1)^{n-1}term, but I don't know why.

Any help is appreciated,

thanks

Sergio

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# Corollary 8: Integration in 'Polar Coordinates'

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