I've lectured integration from the very basics, having covered the following;
- 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
All this is a total of 41 short (5-10 min) lectures (videos), accompanied by example problems etc.
I'm wondering what I should do next, such that it will be natural step forward. Any ideas?