Post #16

Calculus Week Number 16

So this week was a lot of different things. I'll start my post off by saying that I completely did not retain ANY of the information about the trig inverse functions and how to do all of those...I guess the only way I'll remember is by looking at my notes but I forgot my notebook for the weekend so this is all coming from my head...


Okay so the things I do remember

Volume by Discs

Basically you are given an equation, an interval, and what it is to be rotated about...either a line or one of axis's. Your basic steps are to first draw the graph. You need to know what you're looking at. So draw all the graphs as best as you can and determine in a somewhat 3D looking-way what the object or volume you will be finding is. Most of the time, with Volume by disks, you'll wind up with a sphere looking thing. Anyway, so a hint to remembering when to use this is when you have an equation and a line... if it was an equation with an equation you'd use volume by disks because you'd have a hole somewhere. Anyway, the way you do this is you take your equation, square it, and take the definite integral from a to b times by pi.

For a problem where you have to rotate the solid formed by two equations, you basically do it by washers. What you do is you do the top equation squares minus the bottom equation squared. You then take the definite integral from a to b and times that by pi to get your volume.

Both of those are really really simple...it's just a matter of getting it right. Sometimes you have to shift it because you always want it to be rotated about an axis so...what you do is just minus whatever you need from both equations, no big deal.

Anyway, I don't think anyone can really help me with the trig inverse stuff but if you think you can, have at it! :-P