Encyclopedia > Linearity of integration

Article Content

Linearity of integration

A property of the integral which follows from the sum rule in integration and the constant factor rule in integration.

Let f and g be functions. Now consider:

∫ a f(x) + b g(x) dx

By the sum rule in integration, this is:

∫ (a f(x) dx) + ∫ (b g(x) dx)

By the constant factor rule in integration, this reduces to:

a ∫ f(x) dx + b ∫ g(x) dx

Hence we have:

∫ a f(x) + b g(x) dx = a ∫ f(x) dx + b ∫ g(x) dx

All Wikipedia text is available under the terms of the GNU Free Documentation License

Search Encyclopedia

Search over one million articles, find something about almost anything!

Featured Article

Royalist

... noun or adjective, Royalist, can have several shades of meaning. At its simplest, it refers to an adherent of a monarch or royal family. Of the more specific uses of ...