Application To Indefinite Integrals
For example, if you know that the integral of exp(x) is exp(x) from calculus with exponentials and that the integral of cos(x) is sin(x) from calculus with trigonometry then:
Some other general results come from this rule. For example:
The proof above relied on the special case of the constant factor rule in integration with k=-1.
Thus, the sum rule might be written as:
Another basic application is that sigma and integral signs can be changed around. That is:
This is simply because:
Read more about this topic: Sum Rule In Integration
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