Testwiki:Reference desk/Archives/Mathematics/2010 May 5

{| width = "100%"

|- ! colspan="3" align="center" | Mathematics desk |- ! width="20%" align="left" | < May 4 ! width="25%" align="center"|<< Apr | May | Jun >> ! width="20%" align="right" |Current desk > |}

Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

May 5

line integrals with respect to arc length versus x or y

I'm a little confused how to picture these as opposed to line integrals with respect to arc length. Suppose you have a line through a field that "curls back" or even forms a circle. Normally what I see happen is that an integral with a dx term gets added to an integral with a dy term. But what if you just evaluated one of them? Is it possible? And how would you set its bounds? (You would start at x=0, for example, and end back at x=0.) John Riemann Soong (talk) 21:18, 5 May 2010 (UTC)

If (x(t),y(t)), 0<t<1 is a curve, the line integral with respect to arc length of the function f(x,y) is

$\underset{0}{\overset{1}{\int }}f(x(t),y(t))\sqrt{{\left(\frac{dx}{dt}\right)}^2+{\left(\frac{dy}{dt}\right)}^2}dt$

while the integral with respect to x is

$\underset{0}{\overset{1}{\int }}f(x(t),y(t))\frac{dx}{dt}dt$

Bo Jacoby (talk) 23:22, 5 May 2010 (UTC).

1D projection

It is really easy to make a 2D projection of a 3D shape, but what does a 1D projection of a 2D shape look like? —Preceding unsigned comment added by 93.96.113.87 (talk) 21:56, 5 May 2010 (UTC)

A 1D projection of any shape in any number of dimensions is either a point or a line segment or a collection of points and/or line segments. That's all you can have in 1D space - it's not very exciting. Gandalf61 (talk) 22:23, 5 May 2010 (UTC)

—————————————————— — Knowledge Seeker দ 17:26, 7 May 2010 (UTC)