# Approximating Areas under Curves

#### alane1994

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

$$x_k=a+k\Delta x, \text for k=0,1,2,...,n.$$

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

#### dwsmith

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

$$x_k=a+k\Delta x, \text for k=0,1,2,...,n.$$

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
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.