$ \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\abs}[2][]{\left\lvert#2\right\rvert_{\text{#1}}} \newcommand{\ket}[1]{\left\lvert#1 \right.\rangle} \newcommand{\bra}[1]{\langle\left. #1\right\rvert} \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\dd}{\text{d}} \newcommand{\dv}[2]{\frac{\dd #1}{\dd #2}} \newcommand{\pdv}[2]{\frac{\partial}{\partial #1}} $
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Mean Value Theorem for Integrals

Let $S\subseteq\mathbb{R}^n$ be a nonempty, compact, and connected set that has content. For any continuous function $f:S\to\mathbb{R}$, there exists $\vec{c}\in S$ such that $\int_S f(\vec{x})d\vec{x}=f(\vec{c}\mu(S))$.

Concepts

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Hypothesis

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Results

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Proof

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Mean Value Theorem for Integrals

Let $S\subseteq\mathbb{R}^n$ be a nonempty, compact, and connected set that has content. For any continuous function $f:S\to\mathbb{R}$, there exists $\vec{c}\in S$ such that $\int_S f(\vec{x})d\vec{x}=f(\vec{c}\mu(S))$.

Concepts

Coming soon

Hypothesis

Coming soon

Results

Coming soon

Proof

Coming soon
FullPage
result
concepts
hypothesis
implications
proof
FullPage
result
concepts
hypothesis
implications
proof

Mean Value Theorem for Integrals

Let $S\subseteq\mathbb{R}^n$ be a nonempty, compact, and connected set that has content. For any continuous function $f:S\to\mathbb{R}$, there exists $\vec{c}\in S$ such that $\int_S f(\vec{x})d\vec{x}=f(\vec{c}\mu(S))$.

Concepts

Coming soon

Hypothesis

Coming soon

Results

Coming soon

Proof

Coming soon

Mean Value Theorem for Integrals

Let $S\subseteq\mathbb{R}^n$ be a nonempty, compact, and connected set that has content. For any continuous function $f:S\to\mathbb{R}$, there exists $\vec{c}\in S$ such that $\int_S f(\vec{x})d\vec{x}=f(\vec{c}\mu(S))$.

Concepts

Coming soon

Hypothesis

Coming soon

Results

Coming soon

Proof

Coming soon
FullPage
result
concepts
hypothesis
implications
proof