Calculus II For Dummies, 3rd Edition

Chapter 6

Instant Integration: Just Add Water (And C)

IN THIS CHAPTER

Calculating simple integrals as antiderivatives

Using 17 integral formulas and 3 integration rules

Integrating more difficult functions using more than one integration tool

Clarifying the difference between integrable and nonintegrable functions

In Chapter 5, I show you how to use indefinite integrals to solve area problems framed by the definite integral.

Indefinite integrals are essentially antiderivatives, so the good news here is that you can already evaluate a variety of definite integrals by reversing the differentiation process — a major advance over using the difficult Riemann sum formula.

Throughout the remainder of Calculus II, anti-differentiation becomes your go-to method of evaluating definite integrals. Thus, the problem evaluating indefinite integrals as functions takes center stage.

Now some bad news: In practice, finding indefinite integrals is often a lot trickier than differentiation. In some cases, you’ll need to revisit a variety of algebra and trig tricks from your past. In others, integration ...