genkuroki/2017-06-17-192450sagemath.ipynb

## 2017-06-17-192450sagemath.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "#SageMath"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{2} \\, \\pi + \\pi a - \\pi \\sqrt{a^{2} + a}</script></html>"
      ]
     },
     "execution_count": 23,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "var('x, a')\n",
    "assume(a>0)\n",
    "f(x)=sqrt(x*(1-x))/(x+a)\n",
    "#show(integral(f(x),x))\n",
    "show(integrate(f(x),x,0,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\left(a + b\\right)} \\arcsin\\left(-\\frac{\\sqrt{a^{2} - 2 \\, a b + b^{2}}}{a - b}\\right) - 2 \\, \\sqrt{a b} \\arcsin\\left(-\\frac{\\sqrt{a^{2} - 2 \\, a b + b^{2}}}{a - b}\\right)</script></html>"
      ]
     },
     "execution_count": 24,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "var('x,a,b')\n",
    "assume(a<b)\n",
    "f(x)=sqrt((x-a)*(b-x))/x\n",
    "#show(integral(f(x),x))\n",
    "show(integrate(f(x),x,a,b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "SageMath (stable)",
   "name": "sagemath"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
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 },
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 "nbformat_minor": 0
}
	{
	"cells": [
	{
	"cell_type": "markdown",
	"metadata": {
	"collapsed": false
	},
	"source": [
	"#SageMath"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 23,
	"metadata": {
	"collapsed": false
	},
	"outputs": [
	{
	"data": {
	"text/html": [
	"<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{2} \\, \\pi + \\pi a - \\pi \\sqrt{a^{2} + a}</script></html>"
	]
	},
	"execution_count": 23,
	"metadata": {
	},
	"output_type": "execute_result"
	}
	],
	"source": [
	"var('x, a')\n",
	"assume(a>0)\n",
	"f(x)=sqrt(x*(1-x))/(x+a)\n",
	"#show(integral(f(x),x))\n",
	"show(integrate(f(x),x,0,1))"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 24,
	"metadata": {
	"collapsed": false
	},
	"outputs": [
	{
	"data": {
	"text/html": [
	"<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\left(a + b\\right)} \\arcsin\\left(-\\frac{\\sqrt{a^{2} - 2 \\, a b + b^{2}}}{a - b}\\right) - 2 \\, \\sqrt{a b} \\arcsin\\left(-\\frac{\\sqrt{a^{2} - 2 \\, a b + b^{2}}}{a - b}\\right)</script></html>"
	]
	},
	"execution_count": 24,
	"metadata": {
	},
	"output_type": "execute_result"
	}
	],
	"source": [
	"var('x,a,b')\n",
	"assume(a<b)\n",
	"f(x)=sqrt((x-a)*(b-x))/x\n",
	"#show(integral(f(x),x))\n",
	"show(integrate(f(x),x,a,b))"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 0,
	"metadata": {
	"collapsed": false
	},
	"outputs": [
	],
	"source": [
	]
	}
	],
	"metadata": {
	"kernelspec": {
	"display_name": "SageMath (stable)",
	"name": "sagemath"
	},
	"language_info": {
	"codemirror_mode": {
	"name": "ipython",
	"version": 2
	},
	"file_extension": ".py",
	"mimetype": "text/x-python",
	"name": "python",
	"nbconvert_exporter": "python",
	"pygments_lexer": "ipython2",
	"version": "2.7.13"
	}
	},
	"nbformat": 4,
	"nbformat_minor": 0
	}