would i get full marks for this volumez question? (2 Viewers)

[bleakarcher]

thanks guyz

 

[bleakarcher]

can someone answer. drongoski, hermes, thoth, u guyz anyone by man?

 

[apollo1]

the working out seems fine. (ur handwriting is a bit hard to read) but as long as you got the correct answer, i reakon u wuld get full marks.

 

[largarithmic]

I cant read the handwriting and I dont know the question, but I assume you would if you get the right answer and its not one of those "prove volume = something" questions you'd get full marks.

Does anyone know if you need the preamble to do with etc? Like the limiting sum thing. Because I usually just skip straight to the first line of integration

 

[AAEldar]

I cant read the handwriting and I dont know the question, but I assume you would if you get the right answer and its not one of those "prove volume = something" questions you'd get full marks.

Does anyone know if you need the preamble to do with etc? Like the limiting sum thing. Because I usually just skip straight to the first line of integration

In the Independent marking guide lines you have to have the limiting sum and all that for full marks.

Also bleakarcher, I suggest you try to write a little neater, it is a bit hard to read >.<

 

[LightXT]

Before the integration line,
lim deltax->0 sigma notation with limits, and the integral with a deltax on the end of it.
Then go the integration line.
Sorry if that's a bit hard to understand.

 

[largarithmic]

Before the integration line,
lim deltax->0 sigma notation with limits, and the integral with a deltax on the end of it.
Then go the integration line.
Sorry if that's a bit hard to understand.

It's not hard to understand at all. It's just that we were never taught it in class, I've always completely got away with not doing it, and as far as I'm concerned its a completely unnecessary step logically. The actual integration itself means exactly the same thing as the sum with the limits on it; as in thats actually how you define definite integration. You're basically writing the same thing twice.

 

[bleakarcher]

sorry for my handwriting guys. i usually have a huge piece of fuking writing stating delta V is the volume formed by rotating a typical strip of width delta x and height 2y and yadayadayada. is that necessary lol?

 

[bleakarcher]

btw largarithmic, i recommend u define the volume as the limiting sum of the cylindrical shellz as delta x approaches 0 before going to express the volume in terms of a definite integral. depending on the marking criteria, u may lose marks.

 

[largarithmic]

btw largarithmic, i recommend u define the volume as the limiting sum of the cylindrical shellz as delta x approaches 0 before going to express the volume in terms of a definite integral. depending on the marking criteria, u may lose marks.

Yeah alright Ill probably have to do that in the external exam, but I maintain its unnecessary and stupid mathematically. The fact the Board of Studies would even consider requiring you to do that is indicative that their course isnt very good at actual mathematical understanding; it's as if the statement that V is a limiting sum of deltax things, and the statement that V is an integral dx, are somehow distinct mathematical steps. They're absolutely not and to suggest they're the different indicates a failure of the course to teach understanding as oppose to drill problems

 

[bleakarcher]

its to indicate the origin the definite integral i guess lol

 

[AAEldar]

Yeah alright Ill probably have to do that in the external exam, but I maintain its unnecessary and stupid mathematically. The fact the Board of Studies would even consider requiring you to do that is indicative that their course isnt very good at actual mathematical understanding; it's as if the statement that V is a limiting sum of deltax things, and the statement that V is an integral dx, are somehow distinct mathematical steps. They're absolutely not and to suggest they're the different indicates a failure of the course to teach understanding as oppose to drill problems

I have no doubt that you're abilities are greater than mine, but it seems as if you're not completely understanding the concept. They want you to write it in so they can see that you actually do understand that the volume is found by taking the limit as delta x approaches zero of the limiting sum - it's a conceptual thing.

 

[largarithmic]

I have no doubt that you're abilities are greater than mine, but it seems as if you're not completely understanding the concept. They want you to write it in so they can see that you actually do understand that the volume is found by taking the limit as delta x approaches zero of the limiting sum - it's a conceptual thing.

No I think I understand the concept perfectly well. My argument is that "limit as delta x approaches zero of the limiting sum" and definite integration are EXACTLY THE SAME PROCESS. When I write integral from a to b of f[x] dx, what that statement means is the limiting sum when delta x approaches zero. It's exactly the same as dy/dx being shorthand for lim(deltax -> 0) deltay/deltax, but when doing differentiation questions nobody makes you write that. Similarly when doing non-volumes definite integration, nobody makes you write a limiting sum; its a stupid double standard with volumes questions in particular. Have you ever wondered where the integration sign comes from? It comes from an old-fashioned way to write the letter S, that is S for summa, i.e. sum. The fundamental theorem of calculus is then what links definite integration as a process to anti-differentiate. It's something that I don't think is adequately covered in the course, and this silly charade with volumes question is indicative of the lack of conceptual teaching.

 

[bleakarcher]

yeh i agree now actually, its pretty pointless

 

[bleakarcher]

as eldar had said, it is there more to show the marker u understand wat i going on, ie to show him/her y u are taking the integral at all

 

[largarithmic]

as eldar had said, it is there more to show the marker u understand wat i going on, ie to show him/her y u are taking the integral at all

I'm going to do it anyway in case I get a silly marker

 

[bleakarcher]

lol, ull be thanking me for that extra mark in ur hsc.

 

[Drongoski]

I'm going to do it anyway in case I get a silly marker

largarithmic

You are so mature mathematically for an HSC student. Are you a scholarship student at Grammar?

 

[AAEldar]

No I think I understand the concept perfectly well. My argument is that "limit as delta x approaches zero of the limiting sum" and definite integration are EXACTLY THE SAME PROCESS. When I write integral from a to b of f[x] dx, what that statement means is the limiting sum when delta x approaches zero. It's exactly the same as dy/dx being shorthand for lim(deltax -> 0) deltay/deltax, but when doing differentiation questions nobody makes you write that. Similarly when doing non-volumes definite integration, nobody makes you write a limiting sum; its a stupid double standard with volumes questions in particular. Have you ever wondered where the integration sign comes from? It comes from an old-fashioned way to write the letter S, that is S for summa, i.e. sum. The fundamental theorem of calculus is then what links definite integration as a process to anti-differentiate. It's something that I don't think is adequately covered in the course, and this silly charade with volumes question is indicative of the lack of conceptual teaching.

True.

However in most cases we are deriving the integral (right terminology? lolol you know what I'm talking about..) and this would be the reason why that preliminary step is necessary. As you said though - just include it to make sure you don't lose the mark.

 

[largarithmic]

largarithmic

You are so mature mathematically for an HSC student. Are you a scholarship student at Grammar?

Uh, thank you? Maths is my favourite subject though by a way. And yes I am.

True.

However in most cases we are deriving the integral (right terminology? lolol you know what I'm talking about..) and this would be the reason why that preliminary step is necessary. As you said though - just include it to make sure you don't lose the mark.

I can see why you'd want to draw a little diagram explaining the relationship between deltaV, deltax and x, but I really don't get why you need a limiting sum. It's not really helped by the fact that the statement with the sigma with x = a on the bottom, and b at the top, doesn't actually make mathematical sense because the sigma with the numbers on top/bottom usually only deals with discrete quantities (i.e. integers) as far as I know. I could be wrong on that, though.


On a completely different note, did you guys know that volume doesn't actually exist in the first place? I think that's the main underlying rigour problem with the volumes topic more than anything else.