Alrighty, so this week in calc we learned disks and washers... volume and area. went over that the rest of the week, got some packets to work on. all that good stuff. we also learned how to use the clickers which is SOOOOO cool :-) haha, anyways.
disk-solid object without holes
washer-object with a hole
volume of a disk. given equation, solve for x/y. it tells you in the problem which axis it is about. draw your picture and reflect it. formula for volume of a disk is S r^2 dx. your radius is the equation that's given. area is the same except it's just r not r^2.
so the steps all together for finding volume of a disk: solve equation for variable. draw your picture. plug equation into formula. take integral. tada :)
steps for area are exact same except plugging into area formula.
washers are given two equations. graph them and find out which is on top and which is on bottom. volume of washers formula is S top^2 - bottom^2 dx. area is the same formula except neither top nor bottom is squared. same steps. given equation, solve for variable, plug into formula, take integral. tada :) area, just plug into area equation. (obviously)
what im still confused on is LRAM, RRAM, MRAM. never really caught onto it :/
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All I can say on here is plug into the formula, but I know that doesn't help
ReplyDeleteI can help you at school if you want?
i'll do an example for you, you're a bright girl, you'll catch on. if i can get it, so can you.
ReplyDeleteRRAM: right handed aprroximation
formula= delta x [ f(a + delta x) ... + f(b)]
calculate the right riemann sum for a(x)=3x on the interval [-2,3]
divided into 4 sub intervals. (sub intervals are just how many intervals you're setting up/how many numbers you're plugging in.
deltaX=5/4.. use (b-a)/# of subintervals to find this( so (3+2)/4)
5/4[f(-3/4)+f(1/2)+f(7/4)+f(3)]
5/4[(9/4)+(3/2)+(21/4)+(9)= 81
you just use the formula's, that probably won't help you learn how to do it but i'll just post them up here anyway.
ReplyDeleteThe first formula you need to know is x=(b-a)/n [a,b] with n subintervals. You will need to know this because each of the next formulas require that you know what x is.
LRAM- left hand approximation. (this puts the rectangles used to find the area on the left side of the curve) x[f(a)+f(a+x)+...f(b)]
RRAM- right hand approximation. (this puts the rectangles used to find the area on the right side of the curve) x[f(a+x)+...f(b)]
MRAM- approximation from the middle. (this puts the rectangles right on top of the curve, so that the curve goes through the middle of each one) x[f(mid)+f(mid)+...]
Trapezoidal- this does not use squares, instead it uses trapezoids to eliminate most of the empty space inside the curve, and I think this is the most accurate. x/2[f(a)+2f(a+x)+2f(a+2x)+...f(b)]