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
Websites:
slader.com
appcalc.com