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Approximating Areas under Curves

alane1994

Active member
Oct 16, 2012
126
I am learning this right now, and I am having troubles with something.
For regular partition, the formula in my textbook is this.

[tex]x_k=a+k\Delta x, \text for k=0,1,2,...,n.[/tex]

My question is this, how does one find "k"? It is very important clearly!;)
 

dwsmith

Well-known member
Feb 1, 2012
1,673
I am learning this right now, and I am having troubles with something.
For regular partition, the formula in my textbook is this.

[tex]x_k=a+k\Delta x, \text for k=0,1,2,...,n.[/tex]

My question is this, how does one find "k"? It is very important clearly!;)
$\Delta x = \frac{b-a}{n}$ where $[a,b]$ and n is the number of times you want to divide the interval.

The points in the partition will then be $a, a+\Delta x, a+2\Delta x,\ldots, a+(n-1)\Delta x, b$

Usually you are told how many times to divide the interval.
 

Fantini

"Read Euler, read Euler." - Laplace
MHB Math Helper
Feb 29, 2012
342
Or perhaps you decide, rather than being told. A partition doesn't have to necessarily be divided in parts of equal length, but it's certainly easier. :D