Re: "Integral from zero to infinity"

On Dec 9, 7:50 pm, Pat <n...@xxxxxxxxx> wrote:
Hi,

I was just watching this arrogant person on TV,

Just as a matter of interest: who was this person? What was the
program?

R.G. Vickson


basically just rambling on
about how smart she was, and I heard something that I had to take a second
to think about. I guess she thought it would be impressive to rattle off
an integration, so she said:

"The integral from zero to infinity of sin(x) is -cos(x). Come on,
everybody knows that."

Ok, fine, the indefinite integral of sin(x) is -cos(x) (plus a constant
which she neglected to mention). But by giving those limits, zero to
infinity, doesn't the integral evaluate to zero? The "area under the
curve" for sin(x) definitely adds to zero for any interval of length 2
*pi*n, and I would think that n=infinity would be no different.

Or is there something tricky about the limits (0 ... +infinity)? Does
writing it this way somehow turn a definite integral into an indefinite
integral?

Just curious.

.

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