{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Trapezoid rule using scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.integrate import trapz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example\n",
    "$$\n",
    "f(x) = x, \\qquad x \\in [0,1]\n",
    "$$\n",
    "Exact integral is 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Integral =  0.5\n"
     ]
    }
   ],
   "source": [
    "f = lambda x: x\n",
    "a,b,n = 0.0,1.0,10\n",
    "x = np.linspace(a,b,n)\n",
    "y = f(x)\n",
    "print(\"Integral = \", trapz(y,x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example\n",
    "$$\n",
    "f(x) = x^2, \\qquad x \\in [0,1]\n",
    "$$\n",
    "Exact integral is $1/3$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Integral =  0.33539094650205764\n"
     ]
    }
   ],
   "source": [
    "f = lambda x: x**2\n",
    "a,b,n = 0.0,1.0,10\n",
    "x = np.linspace(a,b,n)\n",
    "y = f(x)\n",
    "print(\"Integral = \", trapz(y,x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For uniformly space points we can just pass the spacing instead of $x$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Integral =  0.33539094650205753\n"
     ]
    }
   ],
   "source": [
    "h = (b-a)/(n-1)\n",
    "print(\"Integral = \", trapz(y,dx=h))"
   ]
  }
 ],
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