This week in calculus i actually understood what we were doing and got most of the clicker work right too! It was a good week and i needed that boost of confidence before i completely turn the other direction when we are preparing for the exam. Which i'm a little, well, really nervous for. So the thing i am so anxious to tell you about is volume and area of discs and washers..they are so easy!
So, i'll say this now: AREA IS THE SAME FORMULA, JUST DON'T SQUARE IT!
Now, lets do a volume problem for discs. What's a disc, well i'll answer that question. It's a SOLID object WITHOUT holes. You will have one equation solved for x or y and it will ask you to find the volume of a solid about either axis and give you certain bounds. You simply draw your picture, plug into the formula, take the integral, and then plug in your bounds.
So, volume of a disc formula:
S (radius)^2 dx
*ps, your radius is the equation that is given :)
Now, what's the area formula?
S (radius) dx
*it's the same thing, just not squared :)
Now, lets talk about washers.
Washers are an object with a hole. You are given two equations and then MUST graph them to find out which one is on top. Then, you plug in the formula, take the integral, and then plug in bounds.
Formula for Volume of Washers:
S (top)^2 - (bottom)^2 dx
Formula for Area of Washers:
S (top) - (bottom)
This has got to be my favorite thing so far in calculus because every problem is the same! I love it!
Now, my question is the LRAM, RRAM, and whatever other nonsense was with that..it was kinda crazy..and i still don't understand it. Can anyone help?
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LRAM-left hand approximation
ReplyDeleteremember to start with the interval all the way to the left and add delta x until you reach your b interval term and substitute that into the original function. add all of those and multiply by delta x:
Dx [f(x+Dx) + … + f(b-Dx)]
RRAM-right hand approximation
same as LRAM, except you start from the right.
Dx[f(b) + f(b+Dx)…f(a+Dx)
TRAM-trapezoidal approximation
remember that delta x is over two and that you should multiply all of the numbers, except your functions of the intervals, by 2.
Dx[f(a) + 2f(a+Dx) + 2f(a+2Dx) +…f(b)]
RRAM is the right hand approximation. The formula: delta x[f(a+deltax)+...+f(b)].
ReplyDeletedelta x is b-a/n
The problem should have a point [a,b] and then give you n which is the subintervals.
You take your a and add delta x. Then take whatever you got and add delta x to it. (If your subinterval is 4 then you do it 4 times.) You should end up with b as your last number.
Then you plug into the equation they give you with each one. Add them all and make sure to multiply by delta x!