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The Calculus Lifesaver by Adrian Banner

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CHAPTER 21 _____________________________

Improper Integrals: How to Solve Problems

Let’s get practical and look at a lot of examples of improper integrals. As we go along, we’ll summarize the main methods. In the previous chapter, we introduced some tests that will turn out to be really useful. To use them effectively, you have to understand how some common functions behave, especially near 0 and near ∞. By “common functions,” I mean our usual suspects: polynomials, trig functions, exponentials, and logarithms. So, here’s the game plan for this chapter:

• what to do when you first see an improper integral, including how to deal with multiple problem spots and functions which aren’t always positive;

• summary of the comparison test, limit comparison ...

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