Estimate the area under the curve using Riemann–Darboux's Method.

EstimateDefiniteIntegral

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     "input": [
      "from math import pi, sin\n",
      "from numpy import linspace\n",
      "\n",
      "def integrate(f, interval, samples):\n",
      "    \"\"\"Compute a definite integral of a function over\n",
      "       an interval using Riemann\u2013Darboux's Method.\"\"\"\n",
      "    delta_x = (interval[1] - interval[0]) / samples\n",
      "    return sum([f(x) * delta_x for x in linspace(interval[0] + delta_x, interval[1], num=samples)])"
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     "prompt_number": 20
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     "input": [
      "# Estimate the area under the curve using progressively smaller delta x.\n",
      "interval = (0, pi)\n",
      "for samples in (50, 100, 1000, 10000):\n",
      "    print \"The integral of sin(x) over 0 to pi is %f when using %u samples.\" % \\\n",
      "          (integrate(sin, interval, samples), samples)"
     ],
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     "outputs": [
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       "stream": "stdout",
       "text": [
        "The integral of sin(x) over 0 to pi is 1.999342 when using 50 samples.\n",
        "The integral of sin(x) over 0 to pi is 1.999836 when using 100 samples.\n",
        "The integral of sin(x) over 0 to pi is 1.999998 when using 1000 samples.\n",
        "The integral of sin(x) over 0 to pi is 2.000000 when using 10000 samples.\n"
       ]
      }
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     "prompt_number": 21
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