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2.9

Hands-on: Numerical integration

We continue studying vectorized operations with numerical integration.

Source code for this exercise is located in numpy/integration/

A simple method for evaluating integrals numerically is by the middle Riemann sum

$S = \int_a^b f(x) dx = \sum_{i=1}^n f(x'_i) \Delta x$

with

$x'_i = (x_i + x_{i-1}) / 2 ; x_0 = a, x_n = b$

Calculate the integral in the interval [0,π/2] and investigate how much the Riemann sum of sin differs from 1.0. Avoid for loops. Investigate also how the results changes with the choice of Δx.