This week in AP Calculus, we learned about volumes using integrals, position and velocity, and areas under curves. This was the beginning of chapter 7, and we will be using these more as the chapter goes along. This relates to previous topics because we are still using integrals. We are just applying them in different ways. It could be leading into more with integrals and even more in-depth topics. I understood area under the curve very well this week. It was probably the simplest topic we learned, and it was necessary to understand when we were learning about volumes using integrals. I didn't really struggle with anything this week. Everything was pretty easy once you understood it. To figure out areas under curves, you have to take the antiderivative of the function on top in relation to the axis and subtract the antiderivative of the function on bottom in relation to the axis. If there is only one function, you just take the antiderivative of that function. You have to make sure that you correctly put in the bounds. This should be the range of values on the function for which you are evaluating the area under. In addition, I exemplified participation in class this week.
This week in AP Calculus, we finished sections 6.1 and 6.2 with a quiz. We also started learning about differential equations and separation of variables. This was important because it finishes up chapter 6 for us. Next week, we will have the test over chapter 6, so we will need to know everything that we went over this week. Everything in chapter 6 relates to each other because it all deals with solving equations using the derivative. I understood everything pretty well this week. Separating variables was a fairly simple concept for me to grasp. I didn't really struggle with anything, but I should review some more before the chapter 6 test next week. When solving a separation of variables problem, you will be given the equation of a derivative. You must separate the y's and dy's from the x's and dx's. Once you do this you should take the antiderivative of both sides and simplify. I thought that my participation was spectacular this week. I still need to look at chapter 6 as a whole and review all four sections to prepare for the test. Once I have done that, I think that I will be very well prepared.
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February 2015
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