Area as a limit of sums, signed areas, additivity and linearity of definite integrals

What this note covers

1. Building an accumulation from rectangles
2. The limit of a sum and its notation
3. Signed area versus geometric area
4. Additivity, reversed limits and zero-width intervals
5. Linearity and the contribution of a constant
6. Reading sampled data and judging an estimate
7. Connected reasoning across Definite integrals
8. Error analysis and final checks for Definite integrals

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