The signed area function and the fundamental theorem of calculus

What this note covers

1. An area that changes with its upper limit
2. Why the derivative recovers the integrand
3. Evaluating a definite integral with an antiderivative
4. Reading the shape of an accumulation function
5. The net-change statement of the theorem
6. Choosing the correct function and checking the result
7. Connected reasoning across Fundamental theorem
8. Error analysis and final checks for Fundamental theorem

8 sections · 10 key terms & formulas · 6 common mistakes