EX_23/23_ex_double_integrals.ipynb

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  "metadata": {
    "colab": {
      "name": "23_ex_double_integrals.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aM3JJr0y_x-F"
      },
      "source": [
        "#Double Integrals and Area Between Curves in Python\n",
        "By using dblquad() method, we can get the double integration of a given function from limit a to b by using scipy.\n",
        "\n",
        "\n",
        "Integrate. dblquad() method. \n",
        "\n",
        "\n",
        "> Return : Return the double integrated value of a polynomial\n",
        "\n",
        "This is my second attempt at working integrals in python, since I have some difficulties in algebra :)\n",
        "\n",
        "let's start:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fIz_Cos3fD0t"
      },
      "source": [
        "## 01 - Integrate:\n",
        "\n",
        "$   f(x,y)=\\int_{0}^{2}\\int_{0}^{x^2}\\ y\\ dydx  $\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "E3fWMG_Bnqe5",
        "outputId": "f768d8e5-db2b-43d1-85fc-41081ab82b42"
      },
      "source": [
        "from scipy.integrate import dblquad\n",
        "import numpy as np\n",
        "\n",
        "def integrand(y, x):\n",
        "    'y must be the first argument, and x the second.'\n",
        "    return y\n",
        "\n",
        "ans, err = dblquad(integrand, 0, 2,\n",
        "                   lambda x: 0,\n",
        "                   lambda x: x**2)\n",
        "print( ans)"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "3.2000000000000006\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hpW12BuohrdN"
      },
      "source": [
        " ## 02 - Integrate:\n",
        "\n",
        "$   f(x,y)=\\int_{0}^{1}\\int_{0}^{x^2}\\ (x+2)\\ dydx  $"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "eHEhnqnmh9Em",
        "outputId": "c753aa7e-c621-4fb4-8eca-b6969afe1e57"
      },
      "source": [
        "from scipy.integrate import dblquad\n",
        "import numpy as np\n",
        "\n",
        "def integrand(y, x):\n",
        "    'y must be the first argument, and x the second.'\n",
        "    return  x+2\n",
        "\n",
        "ans, err = dblquad(integrand, 0, 1,\n",
        "                   lambda x: 0,\n",
        "                   lambda x: 2)\n",
        "print( ans)"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "5.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pujE0pZhifhS"
      },
      "source": [
        " ## 03- Calculate the rectangular area  of the function:\n",
        "\n",
        "$ f(x,y)=\\int_{ x = 2}^{4}\\int_{y =2}^{6}\\ \\ dydx $ \n",
        "\n",
        "$ over $\n",
        "\n",
        "$ (2 <= x <= 4)$\n",
        "\n",
        "$ (2 <= y <= 6)$\n",
        "\n",
        "\n",
        "Here is the graph\n",
        "\n",
        "![image.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4RvtwODKiGM-",
        "outputId": "39979bcb-9c1b-406a-9761-141fa810d290"
      },
      "source": [
        "from scipy.integrate import dblquad\n",
        "import numpy as np\n",
        "\n",
        "def integrand(y, x):\n",
        "    'y must be the first argument, and x the second.'\n",
        "    return  1\n",
        "\n",
        "ans, err = dblquad(integrand, 2, 4,\n",
        "                   lambda x: 2,\n",
        "                   lambda x: 6)\n",
        "print( ans)"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "8.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3Q7DEITwn5Dg"
      },
      "source": [
        " ## 04 - Integrate:\n",
        "\n",
        "$   f(x,y)=\\int_{0}^{2}\\int_{x}^{6-x^2}\\ (3x+2y)\\ dydx  $"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MreO2kFSoL8v",
        "outputId": "d7ef302f-2934-4aba-cc83-ccb74aaa5cca"
      },
      "source": [
        "from scipy.integrate import dblquad\n",
        "import numpy as np\n",
        "\n",
        "def integrand(y, x):\n",
        "    'y must be the first argument, and x the second.'\n",
        "    return  (3*x+2*y)\n",
        "\n",
        "ans, err = dblquad(integrand, 0, 2,\n",
        "                   lambda x: x,\n",
        "                   lambda x: 6-x**2)\n",
        "print( ans)"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "59.733333333333334\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Dv9-MJ5JsEVB"
      },
      "source": [
        "Source: Decimal to Fraction Calculator (online)\n",
        "\n",
        "https://www.calculatorsoup.com/calculators/math/decimal-to-fraction-calculator.php"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8LKCOgWhr99D"
      },
      "source": [
        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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x9vEdLWIsp2J"
      },
      "source": [
        " ## 05 - Determine the area in the First quadrant of the region bounded by :\n",
        "\n",
        "###Given parable: $ f(x)=x^3 $ \n",
        "\n",
        "###And Line: $ g(x)=4x $ \n",
        "\n",
        "$ over $ \n",
        "\n",
        "$ (0<=x<=2) $\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hf6CCPDbtriM"
      },
      "source": [
        "x = np.linspace(0, 3, 1000)\n",
        "def f(x): return x**3"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "63NJf2Gj5Nl2",
        "outputId": "687028d3-c21d-419a-892e-e87e22f5f8d0"
      },
      "source": [
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "plt.plot(x, f(x))\n",
        "plt.axhline(color = 'black')\n",
        "plt.fill_between(x, f(x), where = [(x > 0) and (x < 2) for x in x], color = 'green', alpha = 0.3)\n"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PolyCollection at 0x7fa37f871c10>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6G78d1w05Zof"
      },
      "source": [
        "import sympy as sy\n",
        "x = sy.Symbol('x')"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1YWibNKD5wa0"
      },
      "source": [
        "def g(x): return 4*x"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "KvoMDWEk58-o",
        "outputId": "887d0d54-a675-4808-a7c0-3027cfb6ae14"
      },
      "source": [
        "x = np.linspace(0, 3, 100)\n",
        "plt.plot(x, f(x))\n",
        "plt.plot(x, g(x))\n",
        "plt.fill_between(x, f(x), g(x),  where = [(x >= 0) and (x <= 2) for x in x], color = 'green', alpha = 0.2)"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PolyCollection at 0x7fa375f36350>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PutlsLo95_t0"
      },
      "source": [
        "x = sy.Symbol('x')"
      ],
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "id": "kXgT-u607Ogo",
        "outputId": "e1905e5d-26b4-4539-f64d-8152904d8d0d"
      },
      "source": [
        "# The area is:\n",
        "sy.integrate(g(x) - f(x), (x, 0, 2))"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle 4$",
            "text/plain": [
              "4"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yxTAhejHHYzx",
        "outputId": "324035a4-1c0a-4efd-f5a7-8abebda37f51"
      },
      "source": [
        "print(\"That's it! See how your academic life can be made much easier if you use Python! See you soon in the next episode! Bye!!!\")\n",
        "print('Tutorial: [TODO:LINK GOES HERE!]')"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "That's it! See how your academic life can be made much easier if you use Python! See you soon in the next episode! Bye!!!\n",
            "Tutorial: [TODO:LINK GOES HERE!]\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}