Websites:
slader.com
appcalc.com
This week we finished up with the last and final section to chapter 7. We learned another application technique involving integrals called the "shell method." It is important to remember that it is possible to use washer, disc, or shell methods on a variety of graphs. However, how do you decide which one to use? This is the question I tend to ask myself constantly when solving these kind of problems. Honestly, this is the hardest part for me with dealing with chapter 7, is deciding exactly what equation to use for the certain type of graph. But with practice and drawing in the rectangle somewhat helps me figure it all out. Overall, I would have to say the easiest method for me to use is the shell method. However, what can sometimes trip me up with the shell method is the P(x) value when it is not getting rotated exactly on the x axis or y axis. I get tripped off whether it is x+a a-x x-a ect. I hope for the chapter test I will be able to master this skill better. What I found easy in this chapter is setting up the equation and finding the values in general for the shell method. When you have to rotate the equation over horizontally you must remember it must be in f(y) unlike when you use disc or washer method you do just the opposite. Same goes for vertically, you must take f(x). Once you do this it is fairly simple after you plug in the expression multiplied by the P(x) value and integrate it by the (a vs b) or (c vs d) multiplied by 2 pi. In other words it seems complicated but after you figure out where you are rotating it across and the p(x) value it is fairly simple to just plug in. Next week we will be continuing to review this chapter and wrap up the final lessons for the class before we dive into the AP review. I will not be taking the AP test however I still need to be conscious about my ability to gather and absorb all material learned.
Websites: slader.com appcalc.com
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This week we continued to learn more about chapter 7. We dove into section 7.3 that dealt with revolutions of solids. It is very important to understand the integrals from previous sections of when to integrate either from x or y when setting up the equation formula for solving the volume. We learned two methods in particular. One method we used was called the "disk method". This was the easiest method because all you needed to find was the integral you were integrating and the function to plug into the equation. The second method we used is called the "washer method". This method is very confusing to me. I was absent the day it was taught so I have been a little fuzzy on this topic. However, I get confused of which function/value is the larger R and which one is the little r by looking at the graphs. I am a little nervous going into a test on Monday and being confused on the washer method. For next week I hope to get a better understanding of the "washer method" to solve equations. I believe next week in order to successfully do well in the class I will have to make sure I understand the revolution methods well. The quiz we had earlier in the week I felt I was a little confused on. However, after learning more about these kind of solids on graphs I believe I have a much better understanding therefore should be able to complete a mastery on that quiz pretty well. I believe my participation went well this week. I was engaged in the CCCs and contributed towards my work and helping others when we had a sub. Next week I believe we will learn other methods in solving these kinds of equations with revolutions.
These websites were helpful: slader.com solidsrevcalcclassroom.com To start off with the final (third) trimester of this course we began looking at chapter 7. Chapter 7 is the last chapter to be learned for the Calculus exam. Because of the weird schedule with cancellations of delayed exams we went at a little bit of a slower pace with the two first sections. The first section, 7.1, dealt with applications of integrals. This included interpretation between velocity, acceleration, displacement, ect. Because most of these problems were story problems, I struggled with it the most. For this section it was important to remember the standing, velocity, acceleration, and juel rules for derivatives when solving the story problems for anti deriving. However, i grasp the concept of finding the total distance well. i understood the reason for the absolute values of the integral of velocity to find the the total distance. The reason for the absolute values is because you are adding the positive and negative values not just the displacement mechanism. In 7.2 we dove deeper into integrals but ones where we had to solve for their areas within a plane. These areas varied between finding them inside bounded areas. For solving these problems it was important to remember a few specific rules. I had a little trouble with the problems that had you integrate with respect to y instead of x. I got confused on what places to look for the upper and lower bounds to plugged into the equation. However, with practice with the homework, I got more used to dealing with such complex problems and it began to get easier to grasp. I believe my participation went well this week, and I was engaged to ask questions to problems that I needed extra help on. Next week, I know we will have a quiz over 7.1/7.2 and will continue working on further sections within this chapter. I will have to try my best not to fall behind and get caught up with "senioritis" and stay focused in class. |