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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
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