i need some help in finding xi using the midpoint rule. here is an example problem:

integral from 0 to 1 of (1 + x^4)^(1/2) where n=10

- Jan 26th 2009, 05:29 AMchse720how to find xi(bar) = .5(x(i-1) - xi) using the midpoint rule
i need some help in finding xi using the midpoint rule. here is an example problem:

integral from 0 to 1 of (1 + x^4)^(1/2) where n=10 - Jan 26th 2009, 10:44 PMConstatine11
As you are to use $\displaystyle n=10$ intervals they are each of length $\displaystyle \delta x=[1-0]/10=0.1$ and the mid points of the intervals are the points:

$\displaystyle

x_i = (i-1) \delta x + \delta x/2=(i-1/2)\delta x, \ \ \ i=1, .. , 10

$

and your integral:

$\displaystyle

I \approx \delta x \left[ \sum_{i=1}^{10} (1 + x_i^4)^{1/2} \right]

$

.