# 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.

Department of Mathematics, PO Box 643113, Neill Hall 103, Washington State University, Pullman WA 99164-3113, 509-335-3926, Contact Us