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
Canadian Charter of Rights and Freedoms

... expression and freedom of the press, peaceful assembly[?], and freedom of association subject to the reasonable limitations clause (see above) and the notwithstanding ...

 
 
 
This page was created in 25 ms