Fundamental Theorem

This is the bread and butter of integration. Please practice, practice, practice!
Homework assignment: Larson Ch. 4 Section 4 5-31 odd, 35-51 odd, 53-60 all, 69-91 odd

Fundamental Theorem of Calculus Part 2

The assignment here on Definite Integrals and the Fundamental Theorem is related to the ideas that we have talked about below. This should carry you over until we return next Monday. Please let me know if you have any questions on these before we return. Don't wait till that time to ask! You can comment here or reach me by email.

Today we discussed the Properties of Definite Integrals. A list is posted here:



Also, we started with a justification of the Fundamental Theorem of Calculus Pt. 1. This is portrayed in the diagram below:



This leads to the gray box at the top. We call the Fundamental Theorem of Calculus Pt 1. Please follow the logic



This then leads to the Fundamental Theorem Pt 2.



The following is an example that may help with some of the problems on the FTC part 1. I will also put some videos out regarding these problems over the weekend.

Integrals

Integrals from Known Geometric Formulas HW assignment can be downloaded here.



Rectangular Approximation HW assignment can be downloaded here.

Solutions and HW

Solutions and HW for tonight is Chapter 4.1 Section 1-70 odds.

Derivatives Review Free Response Questions

Free Response Question problem set due 11/18/09.

Take Home Assignment

I have decided that we will follow the progression of the book we have been using to deal with the following topics:

Derivatives of Inverse Functions
Derivatives of logarithmic functions with base b
Derivatives of exponential functions with base b
Logarithmic differentiation
Derivatives of Inverse Trig Functions

These are all covered in chapter 5 after basic integration. We can cover more of Linear Approximation through examples over time. It is not a difficult topic at all and with a little practice you will be great at it.

Instead, for this evening I would like you to complete the 4 problems on the attached Take Home Assignment. The problems are challenging, but definitely within the scope of your capability. You may discuss them, but I would like you to complete them tonight.

Solution for #3 on new group test

Below is a solution for #3. There are two graphics and three videos.

Solutions to Problem Set 3 and a new group test!!!

The solutions to the Problem Set 3 are here! The new group test is here as well. Enjoy! This basically concludes out study of derivatives. We will continue to practice, but starting next week, we move on to bigger and badder things - integration.

Motion Problems

Motion Problems

This is an explanation of Applications of Derivatives problem set #65



Here are the videos that show the detail



And continued



Finally

Test on Applications of Derivatives Wednesday 11/4

Derivatives Problem Set #3 and Applications of Derivatives Problem Set #1 and Solutions are attached here.