Author Topic: Basic Calculus - Help needed  (Read 5093 times)

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Offline Sidoh

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Re: Basic Calculus - Help needed
« Reply #15 on: May 14, 2006, 06:34:27 PM »
Heh, you said "total change" is infinity, but you didn't comment on the actual integral, and I believe you said
"good reasoning, bad wording," which does not seem to be a concession that you were originally incorrect?

I was talking about your wording in your reasoning.  I did comment on the actual integral.  The actual integral is net change.

LaTeX is a special typesetting language used especially by scientific and mathematical journals, but is also used to publish books, write reference manuals, document languages, etc.  LaTeX is used as a standard in academic publishing, and the use of anything else is considered unacceptable.  Using LaTeX2HTML, LaTeX2PS, LaTeX2PDF you can also easily generate really nice looking documents where organization of (hyperlinks, bulleting, etc) is automatically done for you.  I bet that any AP exams (in most subjects) you've seen have been written using LaTeX.

Why does it look nicer?  It just does, I guess :P.  It's more smooth, elegant, spacing is handled better, at the expensive of not having a nice GUI associated with it.  For example, look at the integral you posted, and compare it to ones here: http://arxiv.org/PS_cache/gr-qc/pdf/9309/9309018.pdf.

:).

That's because it's the miniumum size.  MathType looks fine if the size is increased.  It's not designed for the same thing, though.

Offline Rule

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Re: Basic Calculus - Help needed
« Reply #16 on: May 14, 2006, 06:39:23 PM »
When I said "actual integral" I was referring to the integral I asked in my question, not the integral of the absolute value of the sin(x) function.  Also "total change," is not very well known terminology.

Quote from: Sidoh
Good reasoning, bad wording.  That's what I get for trying to do calculus when I'm playing WoW.

Since I wasn't playing wow, it seems like a natural assumption that you were referring to your words.  Whatever though.

Moral of the story: intuition can be dangerous.

« Last Edit: May 14, 2006, 06:45:38 PM by Rule »

Offline Nate

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Re: Basic Calculus - Help needed
« Reply #17 on: May 14, 2006, 06:49:54 PM »
(pi/2)(pi/2)^2=(pi/2)^3

Basically, SinX over the integral from 0 to pi is a half circle.  The area of a half circle is pi(r^2)/2.  Radius is 1/2pi and voila you got your answer.  Tell your teacher he/she is a dumbass and needs to not over complicate an alg 2 class.  3.8757845850374775219345393833877 is the numerical value.

Offline Rule

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Re: Basic Calculus - Help needed
« Reply #18 on: May 14, 2006, 06:52:42 PM »
(pi/2)(pi/2)^2=(pi/2)^3

Basically, SinX over the integral from 0 to pi is a half circle. 

No it's not.

Offline Nate

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Re: Basic Calculus - Help needed
« Reply #19 on: May 14, 2006, 07:07:52 PM »
(pi/2)(pi/2)^2=(pi/2)^3

Basically, SinX over the integral from 0 to pi is a half circle.

No it's not.


w/e the answer is 2 then. 

Offline d&q

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Re: Basic Calculus - Help needed
« Reply #20 on: May 14, 2006, 07:12:07 PM »
I've already known the answer is 2 for quite some time now. I stated it in my original post. My teacher is is quite educated, so don't blame him for your lack of knowledge. All I'm asking is for someone to show the steps for me, since they, haven taken calculus, would be able to show/explain it better than I.
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Offline Sidoh

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Re: Basic Calculus - Help needed
« Reply #21 on: May 14, 2006, 07:16:04 PM »
When I said "actual integral" I was referring to the integral I asked in my question, not the integral of the absolute value of the sin(x) function.  Also "total change," is not very well known terminology.

"Total Change" is the integral of the absolute value.  Think about it ...

Since I wasn't playing wow, it seems like a natural assumption that you were referring to your words.  Whatever though.

:-\

I've already known the answer is 2 for quite some time now. I stated it in my original post. My teacher is is quite educated, so don't blame him for your lack of knowledge. All I'm asking is for someone to show the steps for me, since they, haven taken calculus, would be able to show/explain it better than I.

He's not saying you're wrong.

Offline Nate

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Re: Basic Calculus - Help needed
« Reply #22 on: May 14, 2006, 08:43:51 PM »
You want to see the steps?  Left, Middle or Right?

Offline d&q

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Re: Basic Calculus - Help needed
« Reply #23 on: May 14, 2006, 08:49:55 PM »
I've already known the answer is 2 for quite some time now. I stated it in my original post. My teacher is is quite educated, so don't blame him for your lack of knowledge. All I'm asking is for someone to show the steps for me, since they, haven taken calculus, would be able to show/explain it better than I.

He's not saying you're wrong.


I know, I'm slightly tense right now(research paper and all...), and I disliked the fact that he insulted my math teacher and his curriculum. Can anyone show the full steps of integration please?
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Offline Sidoh

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Re: Basic Calculus - Help needed
« Reply #24 on: May 15, 2006, 12:08:21 AM »
I know, I'm slightly tense right now(research paper and all...), and I disliked the fact that he insulted my math teacher and his curriculum. Can anyone show the full steps of integration please?

Using FTC2 constitutes the full steps of integration.  However, due to its obvious simplicity, I doubt your teacher would accept it as a reasonable answer (unless you provide proof that FTC is true).

I'd provide the proof, but alas, I do not have the time tonight.

Offline Rule

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Re: Basic Calculus - Help needed
« Reply #25 on: May 15, 2006, 12:33:48 AM »
When I said "actual integral" I was referring to the integral I asked in my question, not the integral of the absolute value of the sin(x) function.  Also "total change," is not very well known terminology.

"Total Change" is the integral of the absolute value.  Think about it ...

I don't have to think about it much to realize how ambiguous and unstandard that terminology is.  It could mean net area, it could mean improper integral from -infinity to infinity, etc.

Offline Sidoh

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Re: Basic Calculus - Help needed
« Reply #26 on: May 15, 2006, 12:48:24 AM »
I don't have to think about it much to realize how ambiguous and unstandard that terminology is.  It could mean net area, it could mean improper integral from -infinity to infinity, etc.

It could be so obvious to me because our ciriculum uses it pseudo-frequently; it could be so obvious to me because of the few months of newtonian physics I've been through.  I would guess a combination of the two.

Just to show you that it's not some ultra-obscure term, here's a location that use identical wording:

http://www.kirkwood.k12.mo.us/Parent_Student/khs/jonakst/Packet11/Integralasaccumulatorsolns.pdf

These are frequently used in problems that pose this generic question:

 "Some object travles with an acceleration: <X>."

 "a) How far has the car traveled from its starting point at time <t>?"  <-- Net change
 "b) What is the total distance the car has traveled at time <t>?" <-- Total change

It's also extremely useful in the calculuation of forces, which also have vector-based values.