Chapter 18
Ten “Aha!” Insights in Calculus II
IN THIS CHAPTER
Understanding the key concepts of integration
Distinguishing the definite integral from the indefinite integral
Knowing the basics of infinite series
Okay, here you are near the end of the book. You’ve read every single word that I wrote, memorized the key formulas, and worked through all the problems. You’re all set to ace your final exam, and you’ve earned it. Good for you! (Or maybe you just picked up the book and skipped to the end. That’s fine, too! This is a great place to get an overview of what this Calculus II stuff is all about.)
But still, you have this sneaking suspicion that you’re stuck in the middle of the forest and can’t see it because of all those darn trees. Forget the equations for a moment and spend five minutes looking over these top ten “Aha!” insights. When you understand them, you will have a solid conceptual framework for Calculus II.
Integrating Means Finding the Area
Finding the area of a polygon or circle is easy. Integration is all about finding the area of shapes with weird edges that are hard to work with. These edges may be the curves that result from polynomials, exponents, logarithms, ...
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