# Question: Use Fubini s Theorem to give an easy

Use Fubini's Theorem to give an easy proof that D1, 2f = D2, 1f if these are continuous.

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Use Fubini's Theorem to derive an expression for the volume of a set in R3 obtained by revolving a Jordan measurable set in the yz -plane about the -axis.a. Let g: Rn → Rn be a linear transformation of one of the following types:(a) Let A C Rn be an open set such that boundary A is an (n - 1) -dimensional manifold. Show that N = AU boundary A is an -dimensional manifold with boundary. (It is well to bear in mind the following example: if A = {x ...If M is an -dimensional manifold-with-boundary in Rn, define μ as the usual orientation of M x = Rnx (the orientation μ so defined is the usual orientation of M. If xЄ∂M, show that the two definitions ...If w is a (k- 1) -form on a compact k-dimensional manifold M, prove that ∫Mdw =0. Give a counter-example if M is not compact.Post your question