Calculus II is comprised of two distinct parts:
- Techniques of Integration
When you (or a computer) can algebraically integrate a function, how is that accomplished? Essentially, the Rules of Differentiation are "inverted" to the integral, providing the main strategies for attacking the algebraic integral - when possible.
- When Algebraic Integration Just Can't Be Done
The vast majority of functions cannot be algebraically integrated - there just is no algebraic antiderivative for such functions. The development of "Plan B" for attacking these types of algebraic integrals comes in the form of expanding the way we describe functions, not just with the elementary class of functions including such friends as sin(x), ex, x1/2, etc. but with a more generalized description based upon infinite polynomials. This raises all kinds of questions that have to be studied, but once accomplished, we are able to conquer these algebraic integrals.