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It is expected that students will recognize antidifferentiation (indefinite integral) as the reverse of the differentiation process.
It is expected that students will:
- explain the meaning of the phrase “F(x) is an antiderivative (or indefinite integral) of f(x)”
- use antiderivative notation appropriately (i.e., ∫ f(x)dx for the antiderivative of f(x))
- compute the antiderivatives of linear combinations of functions whose individual antiderivatives are known including:
- ∫k dx=kx+C
- compute ∫ f(ax +b) dx if ∫ f(u) du is known
- create integration formulas from the known differentiation formulas
- solve initial value problems using the concept that if F' (x) =G' (x) on an interval, then F(x) and G(x) differ by a constant on that interval