We will do more examples of using the basic formulas to integrate certain functions. We will apply some of algebraic and trigonometric procedure to write the function in a form that fits a formula. This will require a lot od knowledge, creativity, and perseverance.
Assignment
Seven Problems from the text.
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
The lesson went very well. Josh is grasping the concepts and using his critical thinking skills to solve these problems. The problems require multiple concepts of calculus, algebra, and trigonometry.
We will finish the chapter 6 review problems on page 451. We will begin chapter 7 bt doing integrals that follow a formula. We will also look at algebra processes that enable us to fit a given problem to a particular formula. Examples will be presented also.
Assignment
Problems in section 7.1
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
Today's session went very well. We finished chapter 6 and we made a good start into section 7.1.
We will work through the assigned problems from the text. We will emphasize the details of the methods used to review the topics of volumes and length.
Assignment
none
Session Minutes
90
Minutes Student Attended
90
Lesson Comments
We completed the review of the assignment and began the review of chapter 6 in the text.
More practice problems will be done involving finding the length of a curve. We will include an example involving x as a function of y. as well as examples of y as a function of x.
Assignment
Five problems from the AP test practice problems for chapter 6.
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
We completed examples of finding the length of a curve. All went smoothly.
We will go over the assigned problems to begin the session. We will do more examples of the shell and washer methods of finding volumes. We will begin the study of finding the length of a curve.
Assignment
none
Session Minutes
90
Minutes Student Attended
90
Lesson Comments
We are finished with volumes of revolution. We will work on finding the length of a curve to wrap up chapter 6 in our next session. The final three chapters will begin a change from emphasis on integrals and derivatives.
Example of volumes of revelation using washers and shells were presented. We also looked at volumes using cross-sections of a solid. One example led us to a discussion of hyperbolic functions and catenary curves.
Assignment
7 problems
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
The examples were solved and discussed. The hyperbolic functions were discussed and an example of a catenary curve compared to a parabola was presented. The Gateway Arch in St. Louis, Missouri is an example of an inverted catenary curve.
We will find volumes using calculus. There are three types of problems: the disk method, the shell method, and the washer method. All involve integrals and require multiple steps.
Assignment
none
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
We did an example of each type of problem. This enabled us to compare and contrast the 3 methods With these methods we can derive the volume formulas for a variety of geometric solids including cones, cylinders, and spheres.
