And we are getting close to exams now that another week has come and gone. One week to be exact before exams, so because of this we learned a few more things before we start to review.
We learned about the area of washers and volume of disks, the area between curves, and trig inverse integration.
The area between curves formula is bSa top equation-bottom equation
1. draw the picture of the graphs
2. subtract the two equations from each other
3. put the like terms together and integrate the result
The formula for the volume of disks is S (top)^2 - (bottom)^2 dx
The formula for the area of washers is S (top) - (bottom)
The steps are:
1. Draw the graphs of the equations
2. Subtract top graph's equation by the bottom graph's equation(in disks each equation would be squared)
3. Set equations equal and solve for x to find bounds
4. Plug in the bounds and the outcome of step 2
5. Integrate
The trig inverse integration formulas are: sr=square root
1. S du/sr(a^2-u^2)=-1/sr(u)arcsin u/a +C
2. S du/a^2+u^2=1/du(a)arctan u/a +C
3. S du/u sr(u^2-a^2)=1/du(a)arcsec lul/a +C
For what I need help with is remembering all of this. I can handle these when the formulas and stuff are in front of me but without it sometimes I forget what I am doing so if there are any tricks on remembering these formulas i would appreciate if you would let me know.
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okay so i don't know how to remember trig inverse integration formulas, because i can't remember those myself. haha but disks and washers just take practice.
ReplyDeletethere is no trick to remember that volume is squared and area isn't. you just have to remember that.
but, think about this, any time you have a volume problem, you always have an answer with pi in it, right? whenever you have an area problem, there is no pi in your answer. that's how to remember that pi goes with the volume problems and not with area.
also you got some of your formulas mixed up, .. you got area of a washer right. but what you have for volume of a disk... S TOP^2 - BOTTOM^2 dx ... is actually the volume of washer. remember that volume and area formulas are the same.. except area formulas is not squared
formula for volume of a disk
pi S r(x)^2 dx
formula for area of a disk
S r(x) dx
r=radius. radius is the equation that is given to you.