Thread: Understanding First Fundamental Theorum of Calculus

Hey,

I'm just going over (and over and over) the first FTC and i've come to the part where the Mean Value Thereom is used. In wikipedia's explanation of this thereom i don't quite understand a couple of things and hoped someone might be able to clarify them for me:

1) what is the symbol there that i've labled ? in $\displaystyle G(t) ?(t)$ and what does it mean?

2) What does that ?(t) part as a whole represent?

Thank You

Originally Posted by aceband

Hey,

I'm just going over (and over and over) the first FTC and i've come to the part where the Mean Value Thereom is used. In wikipedia's explanation of this thereom i don't quite understand a couple of things and hoped someone might be able to clarify them for me:

1) what is the symbol there that i've labled ? in $\displaystyle G(t) ?(t)$ and what does it mean?

2) What does that ?(t) part as a whole represent?

Thank You

Are you asking "What does the $\displaystyle (t)$ represent?"

It just means that $\displaystyle G$ is a function given in terms of $\displaystyle t$.

No sorry i meant the random symbol (greek letter?).

Thanks

I think s(he) means phi - Greek alphabet - Wikipedia, the free encyclopedia

Not sure why they went for something more exotic than f...

As for its role in that context... Well, the more particular statement, where phi(t) is removed, is a clear enough analog of the main MVT, and if they'd provided a picture, it would show a rectangle sitting between a and b on the x-axis and a roof somewhere between the heights of the curve at those points. Phi(t) is brought in to generalise that simpler situation...

By the way I'm thinking the OP is looking here http://en.wikipedia.org/wiki/Mean_value_theorem at the first MVT for integration.

Hello again - here's a groovy visual http://demonstrations.wolfram.com/In...nValueTheorem/ showing btw that I was careless to say the roof would necessarily be between the heights of etc. It doesn't show the phi generalisation though.