A contract may pay cash continuously rather than on a few payment dates. Integration adds those small payments and gives their total present value. The same operation turns a probability density into a probability. This lesson builds integrals from sums and explains how antiderivatives and substitution evaluate them. Start with differentiation if the derivative notation is unfamiliar.
Learning objectives. By the end of this note you should be able to:
- interpret a definite integral as the limit of weighted sums;
- distinguish definite integrals from antiderivatives;
- apply the Fundamental Theorem of Calculus;
- integrate powers and exponentials;
- use a simple substitution and interpret the accumulated result.
In this lesson
- From sums to integrals
- Antiderivatives and the Fundamental Theorem
- Substitution reverses the chain rule
- Area gives the discounted total
Before you start
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