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[core/

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Corollaries from Regions and order of integration

All corollaries from Regions and order of integration.

[COROLLARY]

The area of a planar region $\Omega$ is

\operatorname{Area}(\Omega)=\iint_\Omega 1\,dA.

The integrand $1$ gives every point of the region unit weight. Replacing $1$ by a density gives mass instead of area.