Extracting the information

1. Apr 15, 2010

annoymage

1. The problem statement, all variables and given/known data

suppose f(x) = x2 and let I = [0,2]

i) if partition I is subdivided into n subintervals of equal length, write down the length of each subinterval,$$\Delta$$x

ii) if ci , is the left endpoint of subinterval i, find ci . hence find f(ci)$$\Delta$$x

2. Relevant equations

N/A

3. The attempt at a solution

i) length of subintervals, Ta = ($$\frac{2a}{n^2}$$)2 , a=1,2,..,n

ii) i don't understand what the question want, left endpoint of subinterval i, what actually "subinterval i"?? owho help im not really god in english

2. Apr 15, 2010

Staff: Mentor

The interval I is [0, 2]. Its length is 2. If you divide this interval into n smaller pieces (subintervals), each of the same length, how long is each one of the subintervals?

For example, if there are 10 subintervals, each would be 2/10 = 0.2 units in length.
If you know how long each subinterval is you can identify the left and right endpoint of each subinterval. Using my example, if n = 10, the subintervals are [0. 0.2], [0.2, 0,4], and so forth up to the last one, [1.8, 2.0].

You need to work this out more generally, using n subintervals, not a constant number like I used.

3. Apr 15, 2010

annoymage

owh i thought its the length of y, ngahaha, i really need to improve my english,
if in that case, each length delta x = 2/n

i see i see, then ci should be

ci = 2i/n , i = 0,1,2,...,(n-1)

right?

4. Apr 15, 2010

Staff: Mentor

This will give you the left endpoints of the subintervals, yes.