This week in AP Calc we learned about rotating curves. This probably has a technical name and technique but to be honest this week I was mostly winging it and making up my own rules.
To give a brief rundown of this topic, you are basically taking a Riemann sum and turning it into a ton of stacked cylinders.
The volume function for a cylinder A=(pi)r^2h becomes A=(pi) f-int{ f(x)^2 dx} with f(x) being the radius of the cylinder and dx being the infinitely small height.
I understood this and found this part of the work fairly easy. My understanding was not as good when it came to revolving things around different lines and revolving areas defined by multiple lines. When I started doing these functions, I had to graph the function and then work out what exactly they were asking. Anything that was being revolved around a strange axis had to be rotated or moved so it lined up with the x-axis. While I was doing this, I’m pretty sure that I was breaking fundamental rules of math, but I seemed to get the right answer anyway.
Then today during the CCC I had to write out a problem on the whiteboard and show work, and I finally understood the correct way to do it.
That seems pretty common in this class; I don’t understand something but manage to struggle my way to the correct answer, and then a week or two later it just clicks.
To give a brief rundown of this topic, you are basically taking a Riemann sum and turning it into a ton of stacked cylinders.
The volume function for a cylinder A=(pi)r^2h becomes A=(pi) f-int{ f(x)^2 dx} with f(x) being the radius of the cylinder and dx being the infinitely small height.
I understood this and found this part of the work fairly easy. My understanding was not as good when it came to revolving things around different lines and revolving areas defined by multiple lines. When I started doing these functions, I had to graph the function and then work out what exactly they were asking. Anything that was being revolved around a strange axis had to be rotated or moved so it lined up with the x-axis. While I was doing this, I’m pretty sure that I was breaking fundamental rules of math, but I seemed to get the right answer anyway.
Then today during the CCC I had to write out a problem on the whiteboard and show work, and I finally understood the correct way to do it.
That seems pretty common in this class; I don’t understand something but manage to struggle my way to the correct answer, and then a week or two later it just clicks.