# Python ICE 4

Given uniformly spaced points
\(a=x_0\lt x_1\lt \dots\lt x_n=b\),
with \(x_{i+1}-x_i=h\) for every \(i\),
the composite midpoint rule for approximating
the integral of a function \(f\) is given by
$$
\int_a^b f(x) dx\approx
\sum_{i=0}^{n-1} f\left(\frac{x_i+x_{i+1}}{2}\right) h
$$
Write a Python function called `midpoint` to evaluate
a midpoint rule approximate to any function \(f\)
we specify.
We will call the midpoint function
as `midpoint(f,a,b,n)`, with arguments as
in our other approximate integral functions.
For \(a\) and \(b\) we choose, use it to evaluate
\[\int_a^b \sqrt{1+\left(\frac{d}{dx}x^{3/2}\right)^2}\,dx\]
and display the result in a string: "The arc length of
x^(3/2) from ___ to ___ is ___".

Send the result to the instructor at the end of class.

Assignment 3 is posted.