post 19

ok so christmas was good :) can't wait for new years!

three formulas for trig inverse functions:
1) 1/du arcsin u/a + C
2) 1/dua arctan u/a + C
3) 1/dua arcsec absolute value of u/a + C

Now on to volume by disks. First off, what is a disk? It's a solid object!The formula is
pi S[r(x)]^2dx
First you have to sketch the graph. Just plug into your y equals in your calculator and sketch! Depending on what axis it tells you to do the problem on is how you reflect the graph. Once you sketch it, shade the graph and then start working the problem!
Ex: Find the volume of the solid formed by revolving the region bounded by the graph of f(x) = square root of x and on y=0 x=3 about the x-axis.
First you would sketch the graph, which looks like a curved line coming out of (0,0) heading to the right to x=3. You then reflect that about the x axis and shade, which alternatively gives you a shape that looks like half of a football. Now to start the problem. Pi S(0 - 3) (square root of x)^2 dxPi S(0 - 3) x dxPi[1/2x^2] 0 to 3=9pi/2

Volume by washers is the same as volume by disks except it has a hole in it. That means it is bounded by two graphs. The formula for volume by washers is
Pi S top^2 - bottom^2 dx.

also area for both disks and washers is the same as their volume formula except everything that usually is squared, isn't squared.

what i don't understand is lram, rram, mram, and tram and how to use them. it just doesn't click in my head for some reason.

everyone be safe on new years :)