Calculus II Workbook For Dummies

Chapter 5

The Fundamental Theorem of Calculus and Indefinite Integrals

IN THIS CHAPTER

Understanding how the Fundamental Theorem of Calculus, Part 2 (FTC2) connects differentiation and integration

Applying FTC2 to solve definite integrals using indefinite integrals

Making sense of signed area

Seeing how the Fundamental Theorem of Calculus, Part 1 (FTC1) allows you to evaluate area functions

In this chapter, you discover and work with the Fundamental Theorem of Calculus, which provides a practical way to calculate integrals that isn’t dependent on Reimann sums.

To begin, you see how one part of this theorem, the Fundamental Theorem of Calculus, Part 2 (FTC2), connects the two main branches of calculus (differentiation and integration). Then, you begin to work with indefinite integrals, which are expressions that help you to calculate definite integrals.

Next, you discover how signed area on the xy-plane occurs when a definite integral produces a negative value. To finish up, you see how the Fundamental Theorem of Calculus, Part 1 (FTC1) makes sense of area functions.

Evaluating ...