Python ICE 6
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.
The last test will take place at the final exam time on
Tuesday, 12 December, from 1:30-3:30. It will be written as a one-hour (not
50 minute) exam, but you may have the full two hours for it.
In other respects it will be very like the other tests, but
comprehensive - it will emphasize Python, but cover all the
topics we have seen.
There is a
Sample Exam, but be aware that things will have changed somewhat
with the advent of ChatGPT.
Assignment A
is posted.