## Topic outline

### General

INTRODUCTORY DOCUMENTS

- This topic
### Topic 5

**Chapter 5: The Definite Integral**

**ACTIVITIES and EXTRA PRACTICE**Khan Academy practice Riemann sums

**OTHER WORKSHEETS****VIDEOS**This video demonstrates the left rectangle approximation method of the area under the curve.

This video demonstrates the midpoint reactangular approximation method for area under the curve.

This video demonstrates the right rectangular approximation method of finding the area under the curve.

**HOMEWORK SOLUTIONS****REVIEW SOLUTIONS**

### Topic 6

Chapter 6: Differential Equations & Mathematical ModelingNOTES

CALCULAUGH WORKSHEETS

**OTHER WORKSHEETS****VIDEOS**General solution to differential equation.

This video demonstrates how to solve a differential equation.

This video demonstrates how to solve a differential equation with the initial condition.

Solving a differential equation with the FTC 1

This video demonstrates a power function u-substitution.

This video demonstrates a u-substitution with a product of trig functions.

This video demonstrates how to do a u-substitution involving a square root and a rational function.

This video demonstrates how to do a u-substitution using a trig identity.

This video demonstrates a u-substitution that involves a simple trig identity.

This video demonstrates solving an integral using a trig identity along with integrating a constant.

**SOLUTIONS****REVIEW**

### Topic 7

Chapter 7:Applications of Definite IntegralsNOTES

CALCULAUGH WORKSHEETS

**ACTIVITIES/WORKSHEETS****VIDEOS**This video contains the first part of Example 2 found on page 3.

This video contains the second part of example 2 and continues on to Example 1 on Page 4 of notes.

This video demonstrates the area between curves given a closed interval.

This video demonstrates area between curves with no given limits.

This video demonstrates finding the area between curves using two integrations.

View this before you start any of the examples.

This video demonstrates horizontal slicing to find the area between curves.

Using your calculator for horizontal equations.

Use this Khan video to learn how to implement a horizontal slicing to find area between curves, then do the practice problems.

This video demonstrates how to find volume using disks with a rotation around the x-axis.

This video demonstrates finding the volume of a solid of revolution around the y-axis using disks.

This video demonstrates finding the volume of a solid using washers with a given integral.

This video demonstrates finding the volume of a solid using washers with no given interval and the use of a trig identity.

This video completes this section by demonstrating how to do volumes using any cross section.

This video demonstrates the process for developing the definition of the length of a curve.

This video demonstrates how to calculate the length of a curve.

**SOLUTIONS**

### Topic 8

### Chapter: AP Exam Preparation

**FREE RESPONSE SOLUTIONS**SPRING BREAK PRACTICE TESTS' KEYS

**ADDITIONAL WORKSHEETS****CIRCUITS**### HELPFUL SITES FOR REVIEW

Khan Academy has several examples here for optimization problems.

Khan Academy teaches you how to use the discriminant to analyze a quadratic, when you're not sure whether it can be factored or not. Very useful for non-calculator situations.