Learning integration, and have gotten to a certain point. What is the next logical step?

manpreet Best Answer 2 years ago

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.

manpreet 2 years ago