We will review integration by parts, L'Hopital's rule for limits, and improper integrals by doing problems in the text.
Assignment
none
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
We had a very productive review. We are nearing the completion of chapter 7. We are making good progress on the content of AP Calculus. We should have a month to prepare for the AP test in May.
We studied applications of integrals, We did some problems involving the physics concept of work. We also studied L'Hopital's rule for finding limits of indeterminate forms using derivatives. Examples were completed.
Assignment
none
Session Minutes
90
Minutes Student Attended
90
Lesson Comments
We did several problems involving the physics concept of work. We also did examples of using L'Hopital's rule to evaluate limits of indeterminate forms.
We are coming to the end of the integration process. It has been long and tedious, but in the process we also do a lot of derivatives and some limits.We will do problems using the integration by parts method. We will do an example of integration by partial fractions.
Assignment
Five problems on integration by parts.
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
We are both happy to be done with integration. It has been a lengthy process without a lot of applications. We wrestle ready to wrap-up the material needed for the AP test and then focus on reviewing for the AP test.
We will complete or study of trig integrals and apply this concept to the method of big substitution. Examples will be completed and problems will be assigned for homework.
Assignment
Problems from section 7.4 in the text.
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
We completed section 7.3 and worked through examples of trig substitution.
We will do several problems to complete the study of trig integrals. We will do examples of integration by trig substitution. This is a new topic, but it is closely related to the previous topics.
Assignment
Four problems on trigonometric integrals.
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
We completed our lesson outline. We are nearing the end of our work on integration. The process of integration involves application of the previous topics in calculus so it helps review those concepts as we move forward. This is important as Josh prepares for the AP Calculus test in May.
We will review several important trig identities. I will introduce the topic by working with Joshua on solving several basic examples to demonstrate the process. We will then look at examples in the text to practice using the integration techniques.
Assignment
None
Session Minutes
90
Minutes Student Attended
90
Lesson Comments
We had a good start to this topic. The topic will be applied in the next section of the text when we do integrals by trigonometric substitution. We will work both sections together to make valuable connections of these concepts.
We will finally finish this very difficult material. We will discuss the homework problems that were carried over from the previous session. We will begin trigonometric integrals and trigonometric substitution tomorrow.
Assignment
none
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
We finished strong. Joshua has a good understanding of this difficult topic.
We will discuss two integration by parts homework problems. We will review the method and continue working on this topic.
Assignment
Four problems involving integration by parts.
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
We did the two homework problems in great detail. mWe reviewed the method once more time. Four problems were assigned. This is one of the most difficult concepts that we will study.
We will do two more examples involving integration by parts. The first will be a difficult problem that is made easier by following the guidelines for getting it started. The second will be a definite integral that is less demanding. We will also do an introduction to section 7.3 on trigonometric integrals.
Assignment
5 problems from section 7.2.
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
We completed section 7.2 and started 7.3. We will soon be done with integration, it is the most important part of the course. There is a great amount of logical thinking and creativity in solving integrals. Joshua is doing very well with all of calculus.
We will complete our examples of integration using tables by going over the 7 assigned problems. from section 7.1 in the text. We will begin our study of integration by parts and do several examples.
Assignment
Six problems from section 7.2 due Monday.
Session Minutes
90
Minutes Student Attended
90
Lesson Comments
Joshua is really doing well with this difficult material He works hard, focuses on the material covered, and perseveres. He is such a dedicated and wonderful student and person.
