calculus - construction theorem

[Tara Rice]

Hi...

I am a calc II student and up to now have loved calculus. I seem, however,
to be hitting a brick wall with the second fundamental theorem of calculus,
or the construction theorem. This states that
F(x)= the integral from a to x of f(t)dt.

Then the text says that you assume that F(x) passes through the point (0,0).
Does the theorem hold true for any value of a, or does it have to be zero?
In If so, wouldn't you have to say that F(x)-F(a)=the integral from a to x
of f(t)dt? What happens to the F(a) if a is not zero? I just really don't
get this yet. Anyone out there who would like to take a stab at helping me
get this??

I just signed up to tutor, too. I need to understand this before I can help
anyone else!!

Thanks.
Tara

[Wade Ramey]

In article <JSbB5.1795$ks6....@news-west.usenetserver.com>, "Tara Rice"
<taral...@yahoo.com> wrote:

> Then the text says that you assume that F(x) passes through the point (0,0).

Tara, I believe no text says that. Can you state your problem more
clearly? Start by stating the second fundamental theorem exactly.

Wade

[JPM, III]

Yeah, I tried to type up an answer before, but I couldn't. I didn't have
enough information to go on...

[Tara Rice]

Thanks for your efforts to help. I see now that my post was quite vague and
that the main problem was that I really didn't even understand what the
construction theorem stated. I re-read the section in the text, and Wade,
you are right; that's not what it says at all. At any rate, with a little
assistance, I understand it much more clearly now, and I will try to be more
specific (and less frantic) if I post in the future.

By the way, what my text actually says is this:
"If f is a continuous function on an interval, and if a is any number in
that interval, the the function F defined by
F(x)=the integral from a to x of f(t)dt is an antiderivative of f."
(Calculus, Single Variable, Second Edition, Hughes-Hallet, Gleason, et al)

I was looking at the equation as the entire theorem and missing the whole
point.

Tara Rice <taral...@yahoo.com> wrote in message
news:JSbB5.1795$ks6....@news-west.usenetserver.com...

> Hi...
>
> I am a calc II student and up to now have loved calculus. I seem, however,
> to be hitting a brick wall with the second fundamental theorem of
calculus,
> or the construction theorem. This states that
> F(x)= the integral from a to x of f(t)dt.
>

> Then the text says that you assume that F(x) passes through the point
(0,0).