{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.4509382\n",
      "0.0002822507289239055\n"
     ]
    }
   ],
   "source": [
    "from numpy import random,sin,count_nonzero,sqrt\n",
    "N=10000000\n",
    "area=2\n",
    "rng = random.default_rng()\n",
    "\n",
    "x = 2*rng.random(N) # space is twice the length random number in x, but this could be also done with specific numpy distributions\n",
    "y = rng.random(N)\n",
    "fx = (sin(1/(x*(2-x))))**2\n",
    "\n",
    "under_curve = count_nonzero(y < fx)\n",
    "integral = area*under_curve/N\n",
    "error = sqrt(integral*(area-integral))/sqrt(N)\n",
    "print(integral)\n",
    "print(error)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.4513352496062641\n",
      "0.00016667578391630662\n"
     ]
    }
   ],
   "source": [
    "from numpy import random,sin,sum,sqrt\n",
    "N=10000000\n",
    "area=2\n",
    "rng = random.default_rng()\n",
    "\n",
    "x = 2*rng.random(N) # space is twice the length random number in x, but this could be also done with specific numpy distributions\n",
    "y = rng.random(N)\n",
    "fx = (sin(1/(x*(2-x))))**2\n",
    "\n",
    "sumf = sum(fx)\n",
    "sumf2 = sum(fx*fx)\n",
    "\n",
    "integral = area*sumf/N\n",
    "var = (sumf2/N)-((sumf/N)**2)\n",
    "error = area*(sqrt(var)/sqrt(N))\n",
    "print(integral)\n",
    "print(error)"
   ]
  }
 ],
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