Double and triple integrals

Integration over planar or spatial regions accumulates density into total quantities.

Different ways to understand it

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Change of variables
A suitable coordinate change transforms volume elements through the absolute Jacobian determinant.
Line integrals
A line integral accumulates a scalar density or vector-field work along a curve.
Multivariable functions
A multivariable function assigns an output to a tuple of inputs in its domain.
Surface integrals
Surface integrals accumulate scalar densities or oriented flux over a surface.
Antiderivatives
An antiderivative has the given function as its derivative; on an interval, any two antiderivatives differ by a constant.