Rules for Definite Integrals

This final page covers important rules and properties specific to bestimmte Integrale (definite integrals), enhancing the understanding of their behavior and calculation methods.

Key rules presented include:

1. Zero integral when upper and lower limits are the same
2. Interval additivity
3. Sign change when swapping integration limits
4. Constant multiple rule
5. Sum rule

Example: The interval additivity rule is demonstrated: ∫[a to b] f(x)dx + ∫[b to c] f(x)dx = ∫[a to c] f(x)dx

These rules are crucial for simplifying complex definite integral calculations and understanding the properties of definite integrals.

Highlight: The sign change rule, ∫[a to b] f(x)dx = -∫[b to a] f(x)dx, is particularly useful when dealing with integrals where the limits need to be swapped.

The page concludes with practical examples applying these rules, reinforcing their application in solving definite integral problems.

Vocabulary: Intervalladditivität (Interval Additivity) - A key property of definite integrals that allows breaking down integrals over larger intervals into sums of integrals over smaller intervals.