The linearity of integrals refers to the property that allows integrals to distribute over addition and to factor out constants. This means that for any functions $f(x)$ and $g(x)$, and constants $a$ and $b$, the integral can be expressed as $$\int (af(x) + bg(x))dx = a\int f(x)dx + b\int g(x)dx$$. This property is fundamental in understanding how to compute surface integrals and flux, as it simplifies the process of evaluating complex integrals by breaking them into manageable parts.
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