# Unit 5

## Intro

• Integration has a wide variety of applications.

• The unit starts with using integration to find the area between graphs of functions.

• From there, we move into 3-D extensions of graphs to find the volume of solids of revolution using Disk and Washer Method.

• Integration can also be applied to find the average value of a function, analyze the physics of basic rectilinear motion, analyze slope fields, and exponential growth and decay.

## 5.1 Antiderivatives and Graphing

### 5.1.1 Area Between Graphs of Functions

• Expressed as Functions of x

• Expressed as Functions of y

• Area Between Curves that Intersect at More than Two Points

### 5.1.3 Volumes

• Volumes with Cross Sections

• Squares

• Rectangles

• Triangles

• equilateral

• isosceles

• right

• Semicircles

• Volume with Disc Method

• Revolving Around the x- or y-axis

• Revolving Around Other Axes

• Volume with Washer Method

• Revolving Around the x- or y-axis

• Revolving Around Other Axes

### 5.1.4 Arc Length**

• Distance Traveled

• Arc Length of Curves Given by Parametric Equations

## 5.2 Modeling with Antiderivatives

### 5.2.1 Modeling

• Differential Equations

• Exponential Models with Differential Equations

• Accumulation Functions in Applied Contexts

5.2.2 Straight-Line Motion*5.2.3 Logistic Model**5.2.4 Parametric and Vector-Valued Motion Equations**5.2.5 Work**5.2.6 Center of Mass**

## Videos

### 5.1.4 Arc Length**

• coming soon...

### 5.2.1 Modeling

• coming soon...

### 5.2.2 Straight-Line Motion

• coming soon...