Summary
Integration is the process of finding the original function f(x) from its derivative f'(x), known as the anti-derivative or integral. It is the reverse of differentiation and involves adding an arbitrary constant 'C' because differentiation removes constants. Indefinite integration refers to integration without specific limits, resulting in a family of functions differing by a constant.
- Integration — the reverse process of differentiation Example: Finding f(x) from f'(x)
- Anti-derivative — another term for the integral of a function Example: f(x) + C
- Arbitrary constant — a constant added during integration Example: C in f(x) + C
- Indefinite integration — integration without limits Example: ∫f'(x) dx = f(x) + C
Exam Tips
Key Definitions to Remember
- Integration is the reverse of differentiation
- Anti-derivative is the integral of a function
- Arbitrary constant is added during integration
Common Confusions
- Forgetting to add the constant 'C' in indefinite integration
- Mixing up definite and indefinite integration
Typical Exam Questions
- What is the integral of f'(x)? f(x) + C
- How do you find the constant of integration? Use a given point on the curve
- What is indefinite integration? Integration without limits
What Examiners Usually Test
- Understanding of integration as the reverse of differentiation
- Correct application of integration rules
- Ability to find the constant of integration using given conditions