Quadrature_Practical_2.ipynb

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      "Quadrature practical 2 - quadrature rules"
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      "1. Integrate $f(x) = 2x^3$ between 1 and 5. \n",
      "2. With two equal intervals, use the midpoint and trapezoid and to approximate $f(x)$. Show that the midpoint rule is roughly twice as accurate as the trapezoid rule.\n",
      "3. Demonstrate that Simpson's rule integrates cubics exactly by calculating it for $f(x)$ with two intervals.\n",
      "4. Show that Simpson's Composite Rule and Weddle's rule both produce the same result.\n",
      "5. Show that the two forms of Simpson's rule are equivalent:\n",
      "\n",
      "\\begin{equation}\n",
      "S = \\frac{2}{3}M + \\frac{1}{3}T\n",
      "\\end{equation}\n",
      "\n",
      "\\begin{equation}\n",
      "S = \\frac{h}{6}\\left ( f \\left ( a\\right ) + 4f \\left ( c\\right ) + f\\left ( b\\right )\\right )\n",
      "\\end{equation}"
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