Chapter 8  Applications of Definite Integrals"Today we can finesse the antidifferentiation step with programs like NINT, but the modeling step is no less crucial. Ironically, it is the modeling step that is thousands of years old. Before either calculus or technology can be of assistance, we must still break down the irregular whole into regular parts and set up a function to be integrated. We have already seen how the process works with area, volume, and average value, for example. Now we will focus more closely on the underlying modeling step: how to set up the function to be integrated."
(Finney, Ross L., Franklin D. Demana, Bert K. Waits, and Daniel Kennedy. "Chapter 8." Calculus: Graphical, Numerical, Algebraic. 5th ed. N.p.: Pearson Education, n.d. 385. Print. AP Edition.) 
Chapter 8 reallife math connection.

Lesson 8.1  Accumulation and Net Change
This lesson will teach students to apply the definite integral to problems involving motion and use the definite integral to solve problems involving accumulation. Lesson 8.2  Areas in the Plane
This lesson will teach students to apply the definite integral to solve problems involving areas. Lesson 8.3  Volumes
This lesson will teach students to apply the definite integral to solve problems involving volumes. 
Lesson 8.4  Lengths of Curves
This lesson will teach students to apply the definite integral to solve problems involving lengths of curves. Lesson 8.5  Applications from Science and Statistics
This lesson will teach students to apply the definite integral to solve problems involving work, fluid pressure, and probabilities. 