For $x\in\mathbb{R}^n$, $u\in\mathbb{R}^n$ and $0<c<\Vert u\Vert$, how could I compute (or find the upper bound of) the following integral $$\int_{x^\top x =1,~\vert u^\top x\vert\leq c}1dx.$$
Any help would be highly appreciated!
2026-03-30 18:20:15.1774894815
Integration over the intersection of a hypersphere and half spaces
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