# Unit 5

## Intro

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.

## Unit 5 Podcast (coming soon)

Unit 5 Podcast (coming soon)

## 5.1 Antiderivatives and Graphing

5.1 Antiderivatives and Graphing

- Expressed as Functions of x
- Expressed as Functions of y
- Area Between Curves that Intersect at More than Two Points

- Volumes with Cross Sections
- Squares
- Rectangles
- Triangles
- 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

- Distance Traveled
- Arc Length of Curves Given by Parametric Equations

### 5.1.5 Area of a Region Bounded by Two Polar Curves**

5.1.5 Area of a Region Bounded by Two Polar Curves**

## 5.2 Modeling with Antiderivatives

5.2 Modeling with Antiderivatives

- Differential Equations
- Exponential Models with Differential Equations
- Accumulation Functions in Applied Contexts

### 5.2.2 Straight-Line Motion

5.2.2 Straight-Line Motion

### 5.2.3 Logistic Model**

5.2.3 Logistic Model**

### 5.2.4 Parametric and Vector-Valued Motion Equations**

5.2.4 Parametric and Vector-Valued Motion Equations**

### 5.2.5 Work

5.2.5 Work

### 5.2.6 Center of Mass

5.2.6 Center of Mass

## Videos

Videos

### 5.1.1 Area Between Graph of Functions

5.1.1 Area Between Graph of Functions

### 5.1.2 Average Value of a Function

5.1.2 Average Value of a Function

### 5.1.3 Volume

5.1.3 Volume

### 5.1.4 Arc Length**

5.1.4 Arc Length**

- coming soon...

### 5.2.1 Modeling

5.2.1 Modeling

- coming soon...

### 5.2.2 Straight-Line Motion

5.2.2 Straight-Line Motion

- coming soon...