How do I find error bounds for approximate integrals? (image included).

Question

anonymous · Answer

attachment

anonymous · Answer

More specifically, how do I get "K"? :/

amistre64 · Answer

where is example 1?

anonymous · Answer

one moment!

anonymous · Answer

Here it is. Example 1

amistre64 · Answer

$$K\ge|f''(x)|$$

anonymous · Answer

So I keep differentiating until I get a constant?

anonymous · Answer

I don't really understand.

amistre64 · Answer

you have an interval from a to b|dw:1334378877377:dw|

amistre64 · Answer

x rests between this interval right?

anonymous · Answer

Correct.

amistre64 · Answer

$$a\le x\le b$$
$$\frac{a\le x\le b}{x}$$
$$\frac{a}{x}\le 1\le \frac{b}{x}$$

anonymous · Answer

So, this is equal to K? What is K supposed to be?

anonymous · Answer

As in, what does it represent?

amistre64 · Answer

Im not sure what it represent at the moment, im just trying to follow the information

amistre64 · Answer

do we have a different problem with an answer thats chkable so that we can play with it?

anonymous · Answer

Simpson Rule, but i think this may do.

anonymous · Answer

And this is the error bound formula for Simpson rule

amistre64 · Answer

i think the K is a maximum for f'' .... but i cnt be sure yet

amistre64 · Answer

Suppose that the second derivative f'' is continuous on [a, b] and suppose that |f''(x)| <= M for all x in [a, b].  Reads to me like M is a max

amistre64 · Answer

or K in this case

amistre64 · Answer

anonymous · Answer

Ah ha! That link helped. M does appear to be a max.

amistre64 · Answer