[BUG] The Valley

[Stuart Boersma]

The last two times I've taught second quarter calculus, I've made use of
the "use what you know" philosophy when it comes to arc-length
integrals.  The book (Hughes-Hallett) gives two formulas for arc-length,
one for parametric curves, one for graphs of functions.  Instead, I took
the approach of giving them just the infinitesmal verison (ds =
sqrt(dx^2 + dy^2)) and emphasize that this will work for any situation. 
The only drawback is that one cannot put limits on the definite integral
until AFTER the integrand has been written in terms of a single
variable.  Then, of course, the limits you choose depend on the variable
you have isolated.  If effect, they are doing line integrals!

I would assume that the main argument for keeping the subscript C in
the line integral is to distinguish it from the indefinite integral
symbol! 

>>> Tevian Dray <tevian at math.oregonstate.edu> 3/17/2004 12:36:37 PM
>>>
> Just a minor point:  In problem number 2 students are asked to choose
a
> curve.  In problem 3 they are asked to evaluate a line integral
along
> the curve C.  However, C was never defined!
> 
> If this lab is to be done as a way to introduce line integrals (as
I'm
> planning), it should probably be made explicit that the curve chosen
in
> problem 2 is in fact C.  

Good point.  This raises an interesting question of notation: Why not
omit
the C altogether?  The integral in problem 3 is clearly a line
integral, and
the problem specifies the location in words.  So why does it feel wrong
to
leave the limits out?  Especially when each group will choose a
different
curve, all of which are being called C.

Tevian
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