@acer 
Thanks

Good exmples for learning the documentmode.

If the student wants to program procedures , then maple input is needed
But using the procedure ability can be handy too in the document mode i think
It seems that there are students now these days who are not using the maple input.

Using the equation labels is for commercial companies who don't have much time for doing their calculations
If this can be done for all sorts of lenghty technical calculations?   

@rlopez 

Thanks

I am glad to that there is 2D inputmode : it makes it easier to study the mathematics were i am interested in.
Did also study some basic programming constructs as maple input, so what you did now is not totally new for me

I can imagine that the student don't like to learn a extra language to learn mathematics
In 2000 there was not other choice when i studied math.
Wondering how this equation z = 4*x^2 - 6*x + 4 in 2D input can achieved ?
I did a attempt , but fill in command : eliminate , but that makes that you must know at forehand this command , lol

For me it doesn't matter if it done in Maple input or 2D input the calculation
But i am curious how it can be done in 2D input, because that is more natural to read the mathemical symbols

I understand the maple input example, so it also faster for me as for you , because 2D input takes longer as pointed out.(update :: see examples ?)
When doing this in Mapleinput you are assured that it is correct, but doing it with 2D input it is more difficult to see if it is the right answer?

In doing mathematics, i like as much as possible in 2D input.
Combining Maple input and 2D input also possible

@Carl Love 
Thanks
 

@rlopez 

Thank you very much for the thoroughly answer of my question.

I do see my book handles this task (on two ways)  also with he parameter t
A line is parametrized with t and by a given line you can then come up with more then one parametrization.
But in your example is direrctly done for the curve as function y=g(x)
Manipulation on expressions is diificult to master for me, but i can learn from this example

Complete square can also of course.be used on 4*x^2 - 6*x + 4

I looked also to eleminate in the help :

The result of this elimination is an expression sequence of lists.  Each list represents a possible elimination of the given variables. => that is not the output on screen ?
A list that has sets as elements in the examples.

The result of this elimination is an expression sequenze of sets in a list as outcome in the examples for the eliminate examples in help?
Probably i am wrong and its deeper under the hood of Maple 

@janhardo 

Seems that a equation of a intersection is needed

Download vb4-blz204-toegepate_wiskunde_deel2.mw

@tomleslie 
Thanks
I was thinking on the same for this adding a t , and add more Pi  like your example
But something went wrong en got a error in the handling of the document mode without prompt
I put a restart at the top of the page and the command was working again
A restart in the middle of the document for a new calculation seems to be not correct, because then i got a error for plotting the helix.  

 

@tomleslie 

Thanks!
Just enough to do my other exercises with different curves  : these circles definitions will be combined with other plots in plot display ( if possible ) 
The vectorcalculus SpaceCurve() circle cannot be transformed into a helix 3D ?    

@tomleslie 

Thanks

-cartesian: in x and y see my example, and in parametric form   
- polar , and in parametric form.: no in3D polar becomes cylindrical
- cilindrical (your example), and in parametric form.

But not with the vectorcalculus possible ?  
A 3D positionvector with no e3 unitvector ( notation be studied in pdf mr. Lopez )

@vv 

First as PathIntegral and x^2+y^2  is a parabolide  ..all intersection planes for z > 0 shows circles   
Plotting the Curve and the scalar function on the same way like is done in the worksheet of mr Lopez
is not that easy.
- i got plot of the parabolide : x^2+y^2
-  now a circle(Curve) in the xoy plane: can be done via with (plots) or with student Vectorcalculus as position vector. ?    
- a green surface is the lift of the circle up to the surface?
 Graphical its clear what to do.

The definiton of a circle is via plots command : spacecurve  

Student vectorcalculus for SpaceCurve command has a tutor ..   

A := PathInt(x^2 + y^2, [x, y] = Circle(<0, 0>, 1));
B := PathInt(x^2 + y^2, [x, y] = Path(<cos(t), sin(t)>, t = 0 .. 2*Pi));
                           A := 2 Pi

                           B := 2 Pi

@Carl Love 
Thanks!
That animation is awesome.
Its confirming alreadymy former  interpretation of a scalar line integral
The vector line integral has still to be studied by me where it is standing for.

Calculs concepts can all be visualized and a proof can be followed too easier,  how it is build up
The Maple software engineers can make these topics too as animation : scalar line integral 
 

@janhardo 
Understanding a mathematical concept is one thing, but translate this into Maple is another thing.
The difficulty as i faced with deciphering the command for a PathIntegral ;)

@vv 
Thanks

Yes, a circulair disk is easier to follow and for getting more insight : a good choice.
A Curve is here a circle with length : 2*Pi*r = 2*Pi
The Pathintegral ( lateral surface of circulair disk ) = lenght circle x heigth = 2*Pi 
So the Pathintergal equals the lenght of the curve     

The spacecurve command argument handling comes in play to define all sorts of curves for a pathintegral  ( not-parametrized and parametrized)

@rlopez 

Thanks
You noticed that with all sorts of integrals involved i loose oversight. 
That a Pathintergal= Surfaceintegral (post vv 7821 )  makes that i ask myself what is that surface in your example although it is not mentioned.( answer: its a surface of a double intergral )

I tried to solve my bookexample on the same way you did, but did not get a plot yet (has to do with the definition as a spacecurve in the xy-plane)
 

@vv 

In case of the plot in the worksheet:  if i give meaning to your text then is the green area ( pathintegral) equals the red area (surface intergal) : correct?  

@vv 

Thanks
I must study my bookexample in the same manner as explained there.
Doing this in Maple on the same way.
Did not made a comparison yet for the worksheet from mr. Lopez, but it is indeed using a surface and that's not used in my bookexample

For me is interesting to see a other solution methode too , so  i am pleased to see other ones.
In my calculus book the example its solved on 3 ways! ( see pdf for one ) 
And learn from the example from mr Lopes ( handling Maple too )  
Handling the iterated integral  / PathInt  commands via context Panel Dialog is not clear for yet what to fill in, but the screenshot explains more    

Looks your formulation is the  Green integral ? what is more advanced then the basic method in my bookexample.
There is also a surface integral formula what is a iterated integral over a area in xy-plane 

 PathInt command and LineInt command  both in vectorcalculus package
PathInt ,using no vector
LineInt , is using a vector