Department of Mathematics

Math 300: Mathematical Computing

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 "final exam" for this course will take place at 8:00 AM on Tuesday, 12 December. This will be an ordinary 50 minute test. It will be comprehensive, but weighted toward the latter half of the semester. As always, paper notes will be permitted, but no electronic devices will be allowed.

A Solution example is available for the quiz.

Assignment A is posted.

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