Calculus II Workbook For Dummies

Chapter 1

An Aerial View of the Area Problem

IN THIS CHAPTER

Measuring the area of shapes with classical geometry

Finding the area of shapes on the xy-plane

Using integration to frame the area problem

In Calculus I, you discovered how to use math to solve a single problem: the tangent problem or slope problem, which involved finding the slope of a tangent line to a function on the xy-graph. Calculus II is also devoted to solving a single problem: the area problem — finding the area of a region of the xy-graph under a function.

In this chapter, you use a variety of simple methods to frame and solve area problems. First, you use formulas from classical geometry to measure the area of familiar shapes on the xy-graph. Next, you discover how to define the area of a region under a function as a definite integral.

To finish up, you put those two skills together, both setting up and solving definite integrals to solve area problems for relatively simple functions.

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Measuring Area on the xy-Graph

People have been calculating the area of shapes for thousands of years. More than 2,000 years ago, Euclid developed a thorough system of geometry that included methods for ...