Re: Info and a Question

Bret Taylor (bret@IAG.NET)
Mon, 19 Aug 1996 22:55:00 EDT

At 09:12 AM 8/19/96 EDT, you wrote:
>Greetings,
>
>
>
>Consider the region bounded above by y = 1/x. Compute the area under
>this curve, above the x-axis, between x = 1 and x = 00 (infinity).
>The "area" of this region is given by fnInt(1/x,x,1,00) and is
>infinite (the improper integral diverges).
>
>However the volume obtained when we rotate this region about the x-axis
>is given by pi*fnInt(1/x*x,x,1,00) = pi.
>
>How do you expain to students that the area is infinite but the volume
>is finite, since the area fits inside the volume?
>
>Have fun! May your semester be full of the joy of teaching.
>
>Brian
>
>________________________________________________________________________
> Brian E. Smith
>Dept of Mathematics TEL: 514-931-8731 Ext 1713
>Dawson College FAX: 514-931-3567
>3040 Sherbrooke St. W. EMAIL: (1) inbs@musicb.mcgill.ca
>Montreal, QC, Canada H3Z 1A4 (2)besmith@dawsoncollege.qc.ca
>-----------------------------------------------------------------------
>I would rather lose in a cause that will someday win, than win in
>a cause that will someday lose -- Woodrow Wilson
>-----------------------------------------------------------------------
>
Brian,

Thanks for all your work. Your question is one I give to my students
annually with the standard question, "This 'can' has a finite volume but an
infinite surface area so that means you could fill it up with paint but
never be able to paint the outside. How can you explain this paradox?"

In ten years, I have had one student give a clear expanation. How about the
rest of y'all?
Bret Taylor Lake-Sumter Community College Leesburg FL

"It matters not the subject taught, nor all the books on all the shelves.
What matters more, yes most of all, is what the teachers are themselves."
John Wooden

John 3: 3 3