This week in AP-Calculus, we learned about solids of revolution. We also took the 7.1-7.2 quiz, and I did pretty good on it. Solids of revolution using the disk method has been pretty easy so far. The concept took some explaining since it involved picturing a three dimensional shape, only using its two dimensional profile. Once I wrapped my head around that, the process was fairly quick. The equation for finding the volume of the shape just uses the equation for the volume of a cylinder, but replaces some parts of the equation with parts of integrals. The equation is pretty basic and can be used for the majority of the problems, even those in terms of y. Basically, the volume is equal to pi times the integral of the function, but you square the entire function. You use the bounds like normal and it will output the volume of the 3D shape created by the function.
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This week in AP-Calc, we learned about integrals as net change and finding area under two curves using integrals. This was the beginning of chapter 7, and like every chapter, there was a lot of new concepts to learn about. Integrating net change was not that hard since we already know about acceleration, velocity, and position. This was one of the first times we actually went into depth about acceleration, velocity, and position. I am glad we are going into depth on these topics since acceleration is an important topic for us to learn about since we all use acceleration to get to school. We also learned about areas between curves and how to find the area using integrals. To find the area between the curves, you subtract the integral of the bottom curve from the integral of the top curve. This was not a difficult topic to learn since we knew everything leading up to it. It uses integral rules that we learned in previous chapters. This is a nice start to a chapter since it is not too difficult and is a nice way to ease into the chapter.
This week in AP-Calc, we learned about slope fields and separation of variables. A slope field is a graph of the slope at all the points on your interval. This will give you a general idea of what the original function will look like. These are not that hard since you plug in the points and graph the slope at that point. Sometimes, you might have to draw a slope field for an equation with both x and y. You still do the same thing and plug the point in and graph the slope at that point. Separation of variables is slightly harder. For that, you need to separate the variables from each other. you need to get all of the on kind of variable on one side, and the other variable on the other side. After that, you can anti-derive and get the original function, but don't forget about the +C. After that you can solve it explicitly or leave it. If you are given a point on the original function, this is the time to plug it in and solve for the +C.
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February 2018
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