{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Trapezoid vs Gauss quadrature for periodic function"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us compute\n",
"$$\n",
"\\int_0^{2\\pi} \\exp(\\sin x) dx\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 2 1.6717412138e+00 1.5277448438e+00\n",
" 4 2.8260084821e-04 2.0275305634e-01\n",
" 6 3.4594549447e-09 1.5148783594e-02\n",
" 8 7.1054273576e-15 1.2229354413e-03\n",
" 10 1.7763568394e-15 2.9323632519e-05\n",
" 12 1.7763568394e-15 3.4262054047e-06\n",
" 14 0.0000000000e+00 1.1795276755e-08\n",
" 16 2.6645352591e-15 4.7241393020e-09\n",
" 18 1.7763568394e-15 1.0296208330e-10\n",
" 20 8.8817841970e-16 2.8332891588e-12\n"
]
},
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n",
"\n"
],
"text/plain": [
"