# 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.

## Unit 5 Podcast (coming soon)

## 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**

## 5.2 Modeling with Antiderivatives

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

### 5.1.1 Area Between Graph of Functions

### 5.1.2 Average Value of a Function

### 5.1.3 Volume

### 5.1.4 Arc Length**

coming soon...

### 5.2.1 Modeling

coming soon...

### 5.2.2 Straight-Line Motion

coming soon...