Centroid for exp(-t)

From: Anand Ramalingam (anand_ramalingam_at_yahoo.com)
Date: 06/09/04 

Date: 9 Jun 2004 11:12:19 -0700

Hi,
I am trying to find out the centroid of h(t) = (1/tau)*exp(-t/tau).
where tau>0
and 0<t<infinity

I used the following formulas to find the (x,y) coordinates of the
centroid.
Cx = integral(t h(t) dt)/integral(h(t)dt) = tau
Cy = integral((h(t))^2 dt)/integral(h(t)dt) = 1/(2*tau)

Assuming the formula is correct, the centroid turns out to be
(tau,1/(2*tau))

If you take tau=1, then the centroid is (1,1/2) which lies *outside*
the curve.

This looks little weird to me. As far as I understand centroid is the
center of gravity, basically the point at which you can balance the
shape. If the point lies outside the shape then how can one balance
it?

Thanks
Anand

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