
Let and
be two functions of
, and let
be a constant. We already know that for derivatives,
and
But since the indefinite integral is just the operation of undoing a
derivative, the same kind of rules must hold true for indefinite integrals as well:
and
And since a definite integral can be found by plugging in the upper
and lower limits of integration into the indefinite integral, the same properties must be true of definite integrals as well.
Example
Evaluate the indefinite integral
Using the additive property, the integral becomes
Then the property of scaling by a constant lets us change this to
We need a function whose derivative is , which would be
, and one whose derivative is
, which must be
, so the result is
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