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Center of mass in a straight rod [duplicate]

I got an assignment to prove that in a straight homogeneous rod, you can always choose a coordinate system in such a way that $\int_S x_1dx_1dx_2=0 $ $\int_S x_2dx_1dx_2=0 $ $\int_S x_1x_2 ...
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A question from Selected Topics in Integral Geometry

I'm referring to Gel'fand, Gindikin, and Graev's Selected Topics in Integral Geometry, pages 4-5, section 1.4 (see here and here). Now in page 5 they write that: $$dx_1 dx_2 = d(\xi_1 x_1 +\xi_2 x_2 ...
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Integral Geometry Reference Request

I am looking for a good introductory reference (book, lecture notes, survey article) on integral geometry. I am especially interested in the Crofton formula in $\mathbb{R}^n$ and its extensions to ...
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The Cauchy-Crofton Formula

I am trying to understand the most basic formula from integral geometry. I have been looking at this website. The problem is things aren't working out for very simple examples. The circle works ...