Chapter 12
Forging into New Areas: Solving Area Problems
IN THIS CHAPTER
Evaluating improper integrals
Solving area problems with more than one function
Measuring the area between functions
Finding unsigned areas
Understanding the Mean Value Theorem and calculating average value
Figuring out arc length
With your toolbox now packed with the hows of calculating integrals, this chapter (along with Chapters 13 and 14) introduces you to some of the whys of calculating them.
I start with a simple rule for expressing an area as two separate definite integrals. Then I focus on improper integrals, which are integrals that are either horizontally or vertically infinite. Next, I give you a variety of practical strategies for measuring areas that are bounded by more than one function. I look at measuring areas between functions, and I also get you clear on the distinction between signed area ...
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