Volumes by slicing
First of, getting the derivative and the second derivative. Well, we all know how to get them at this point, we're probably good at it, by now, considering myself! (can you believe that? :D) Then the difference between the net and total distance was tackled. The second question involved integrating the area of a region "S" enclosed by graphs f and g, which is by the way an easy thing to do because this whole stuff is not new to us, right? But (a BIG BUT) when we came to the part where we had to find the volume generated by rotating region "S" around the x-axis... Okay, where am I now?
it wasn't very easy for me to understand this chapter because first and foremost, I couldn't picture out the image we were visualizing. So that's probably one note to greatly put everyone's attention to, VISUALIZE. ;) It will absolutely be hard to go through all these questions if merely knowing what it looks like is not met.
Two things I've learned that I thought were new:
- the slicing task results to a WASHER (well, not always)
- the concept of BIG R and small r. (its not new but subtracting R - r is pretty unfamiliar to me, but then again, I know everyone understands it)
> memorize the volume formulae (it helps, big time!)