# Questions tagged [multiple-integral]

For questions regarding computation and results related to integrals in at least 2 variables.

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### Question about Lemma 19.1 in Munkres' Analysis on Manifolds

In Munkres' Analysis on Manifolds, page 162 Lemma 19.1 Step 2 it states: Third, we check the local finiteness condition. Let $\mathbf{x}$ be a point of $A$. The point $\mathbf{y}=g(\mathbf{x})$ has a ...
• 174
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### Stokes’ theorem question for cylinder-like surface with two disjoint boundaries

Q: Consider $S=\{(x,y,z)\mid x^2+y^2+z^2=25,\; 0≤z≤4\}$ and the vector field $\vec F(x,y,z)=(y,-z,x)$. Use Stoke’s theorem to calculate $\iint_S(\nabla \times \vec F )\cdot \vec n \; dS$ $\vec n$ is ...
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### Theorem 16.5, Munkres' Analysis on Manifolds [closed]

In Munkres' Analysis on Manifolds, page 142 Theorem 16.5 it states: $$\int_{D}f\leq\int_{A}f$$ at the end of that page. Here, $D=S_{1}\cup\cdots\cup S_{N}$ is compact since $S_{i}=Support\phi_{i}$ and ...
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