Calculus › Section E · Integrals › Topic E.4
The fundamental theorem of calculus
Derivatives measure how fast things change; definite integrals add up how much has changed. This theorem shows they are inverse processes, and it turns hard area problems into a few lines of algebra.
In this topic
- Two big ideas, one bridge
- The accumulation function
- Part 1: accumulation and rate
- Worked example: Part 1 with a chain
- Part 2: evaluating definite integrals
- Worked examples: Part 2
- The net change theorem
- Average value and the mean value theorem for integrals
- Signed area and total area
- Worked example: a function defined by an integral
- Common mistakes to avoid
- Key takeaways
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Standards: 6