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
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]
$
.