I've learnt the following in terms of integration;
- What are integrals, and what do they represent?
- Indefinite integrals as the opposite of derivatives
- Using the power rule for derivatives to provide the power rule for integration
- Integral as infinite sum
- Area under curve, and area between two curves
- Volume of solid of revolution
- Integration by substitution
- Integration by parts
- Integration by partial fraction expansion
- Improper integrals
I'm wondering where to go from here. I know the basics of numerical methods, and the fundamental theorem as well. I'm looking to go further in terms of analytical integration, but I don't know which topic would be next. Any ideas?
EDIT: I've checked the syllabus for AB/AP calculus, but it only lists very vague ideas of the concepts, and not sub-topics.