Error calculation in definite integral approximation

[Demosthenes]

The error when using a rule for approximating a definite integral is given by the following equations:

http://img83.imageshack.us/img83/1827/approxhh0.jpg

I have no idea how these were derived, but these were the equations given to us. We were told that we'd learn how they were derived in a numerical analysis class. This is all fine and good, but I'm not sure exactly how I'm supposed to pick the x value to calculate the coefficient k to find the largest error that there can be. The book offers a very convoluted explanation of this, and it almost seems to arbitrarily pick an x for the calculation of k at one of the limits of integration. This seems to make sense, but I'm not sure exactly how it picks whether to use the a value as x or the b value. If anyone could explain this to me, or link me to a site which has a decent explanation of this, I would greatly appreciate it.

[!King_Amazon!]

I can't help you because you just blew my fucking mind.

Is this one of those classes where the teacher talks and then all of the students become retarded and start banging their heads on the desks while chanting "definite integral approximation blarg blarg blarg"?

[Tyrannicide]

Did I just get raped?

Seriously, wtf is that shit...now I know why I hated math and plan to stay the fuck away from it....

Fuck, good luck man...im lost.

[Lenny]

I understand a bit of it - we've just started integration.

Is it just the first part of each statement up to "where k=..." that you've got to learn how they were derived? My textbook explains from "where" onwards. I'll have a looky to see if it has the first part of the equation.

[Grav]

Isn't x just a variable? It represents all the values that fall within the bounds of a and b...

[Demosthenes]

Seriously, we're not in the chat section...

And no, x is apparently supposed to be the x where f(x) is the upper bound of the 2nd or 4th derivative to calculate k.

[MightyJoe]

http://www.ltcconline.net/greenl/courses/105/Antiderivatives/NUMINT.HTM

Not too sure if this will help at all or not, I'll try to look at this tomorrow once I'm awake.

[Demosthenes]

http://www.ltcconline.net/greenl/courses/105/Antiderivatives/NUMINT.HTM

Not too sure if this will help at all or not, I'll try to look at this tomorrow once I'm awake.

Thanks! That helps a lot. In fact:

B = max |f ''(x)|

was exactly what I was looking for. I'm just...not looking forward to taking the fourth fucking derivative of e^x^2;