= Domain of integration
{title2=$D$}
= Integration region
{synonym}
= Region of integration
{synonym}
The domain of integration is the set $D$ over which an <integral> is taken. For a <multiple integral>, inequalities or parameter ranges specify which points belong to $D$; a <change of variables> transforms both these bounds and the integration element through its <Jacobian determinant>. For example, a polar region $c\leq r\leq1+\cos\phi$ exists only at angles where $1+\cos\phi\geq c$.
The set over which an <integral> is taken. For a <double integral>, boundary inequalities describe the allowed coordinate pairs, and slices of this set determine the limits in an <iterated integral>. The domain need not be a rectangle or connected. A <change of variables> transforms both the integrand and this set.
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