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Multivariable calculus

Course: Multivariable calculus>Unit 5

Lesson 11: Divergence theorem proof

Divergence theorem proof (part 3)

Evaluating the surface integral. Created by Sal Khan.

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• why did we take the S3 such that it's normal vector has no k^ component where as there can be the case when it's not so, for example section of a cone above xy-plane. Also is it necessary that we should be taking surface such that it's domain for f1 and f2 are same, as in this video we have taken for both f1 ans f2 as D.
• if it was a cone, the pointy part would be S2, which would touch S1, so there would not be an S3 (and thus no k^ component). As for having the domains be the same, yes, to be a type I, II, or III, the two functions must both be applied to the same region.