Sektorenformel nach Leibniz

Die Sektorenformel
Die Formel zur Berechnung des [b]Flächeninhalts [/b]eines [b]Sektors [/b]zwischen zwei Radiusvektoren und der Kurve lautet für[br][table] [tr][br] [td][b]Funktionen in Polardarstellung[/b] [br][math]r: I \mapsto \mathbb{R}; \varphi \rightarrow r\left(\varphi\right)[/math][br][br][math]\mathbf{A=\frac{1}{2} \cdot \int_{\varphi_1}^{\varphi_2} {\left(r \left(\varphi \right)\right)^2} d\varphi}[/math][/td][br] [td] 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[/img] [/td][br] [td][b]Funktionen in Parameterdarstellung[/b][br] [math]f: I \rightarrow \mathbb{R}^2 ; t \mapsto \left(x\left(t\right),y\left(t\right) \right)[/math][br][br][math] \mathbf{A = \frac{1}{2} \cdot \int_{t_1}^{t_2} \left(x(t) \cdot \dot{y}(t) - y(t) \cdot \dot{x}(t) \right) dt= \frac{1}{2} \cdot \int_{t_1}^{t_2} \begin{vmatrix}[br]x & y \\[br]\dot{x} & \dot{y}[br]\end{vmatrix} dt}[/math][/td][br][/tr][br][/table][br]Die Herleitung der beiden Formel ist weiter unten zu finden.[br][br][i]Hinweis: [br]Zur Eingabe einer anderen Funktion im ersten Applet muss das Zeichen für φ mit Copy und Paste eingefügt werden.[/i]
Sektorenformel nach Leibniz für Funktionen in Polardarstellung
Aufgabe
Berechne den Flächeninhalt des Sektors der Funktion [math]r:\mathbb{R} \rightarrow \mathbb{R}; r \left( \varphi \right) = a\cdot cos\left(\varphi\right)[/math] mit [math]a=2[/math] von [math]\varphi_1=0[/math] bis [math]\varphi_2=3.14[/math].
Sektorenformel nach Leibniz für Funktionen in Parameterdarstellung
Aufgabe
Berechne den Flächeninhalt des Sektors der Funktion [math]f: \mathbb{R} \rightarrow \mathbb{R}^2 ; t \mapsto \left(x\left(t\right),y\left(t\right) \right) = \left( 1+a \cdot cos(t) , sin(t) \right) [/math] mit [math]a=2[/math] von [math]t_1=0[/math] bis [math]t_2=3.14[/math].
Herleitung der Formeln
[br][table][tr][td][b]Polardarstellung[/b][/td][td][/td][td][b]Parameterdarstellung[/b][/td][/tr][tr][td] [br] 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[/img][/td][td][/td][td] 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AnJtNVTPqYQbgThRogIDsBUF8CjR49IQlpYWNCOQ2WuBEs2PgQwIZm26akHpwg3YonPEqYVRMqx2WxqQlJE1GCROnBhI0QAE5JRo7Kr2NYnrQk34tqza4wqMBByc3MjO0nyaHEGNbBI40cAE5JRGz9MeEgGBygoLWBUgYHQkydPSEKam5tXVFQwqIFFGj8CmJCM2pgMDrA7cDcjaWZCHA5n5syZJCfDw8OZVcJSjRwBTEjxDZxTlDNq46gJOyZEJ0eLl5ZEwtXVlSTkgQMHJKmHZRstApiQ4pv29IPTKlYqus66DIMDiNf4VSIiIoIk5IwZM3hPbvtajv/f5BDAhBTT5Fzg6jrrqlip/Hn/TzGikhdXVlZScT2ePHkiuQJco7EhgAkppkWfpjztNr9bf8f+2YXZYkSlKt6zZw/ZSeIty1Lh19gqyZOQXl5eWl+uoUOHNhqc1pxfozRTyf6EfR09UXBwMEnI+fPn15EJrFaBEJAnIanH1tLSotIKnSgsK5Q6OADDB8/Pzx87dmz79u3btGlT53HNCwqgQG7TNgwfEItJhAAmpCi4ZAkOIEovTxmHw2nTpo35L7/M/+WXDh06JCcn8xTKO5mXBxs2yFsp1idPBDAhRaFJBgc4fPOwKCHZynJzc5WVlCKVlGLat9fQ0AgJCZFNn7jaPj7g4yNOCJd/MwQwIYVC//bD24m7J47YMCIlL0WokDwKFvfp86xZs7fNmrVp0+bTp09iVKalwdy5MGeO9P+6dQP7uvokFuM8LhaHACakUISO3D1CuBGrLq0SKiGXguJijoXFJTW1nO++s54wITIyUrzWjAxISpLyX2QkmJpCfLx4KxJJFBXB6tUS1WgSwvn5sEf80S+8UGBC8qJRky6rLDM/Zk64Ebdf367JrYvUiRNgZnZ5zpz85s2PDxz455/yn+2s5fXixfIf16moAEND+ZO8lt8KexMUBJKcQYgJKbilb7++TbgR5sfMyyrLBEvIJTc5GQgCLlx4vG3bxxYtolRVVzo5Saz4jz9g/XpGtd69g5s3GUlKJOTsDC58J7pfuwbDhkGOBJHdBdsU+3T+/vDhg+C6/Lly8UpSl+bPB8ZjdZiQ/I2Gclb/vZpwI9zuShnrUbBS/tyNG2HhQkhPz/Xw+PDDD0lt266YMKG0tJRfUGjOx4+wezf88IMEP0qhuqQqSE2FH3+E3Fx65dOnoWNHSE+n50t0L/bpuFxk/SmjA8iQZdm9ksKliAiYPZvhc2NCCgAq5WOK0REjwo2IzYwVUCynrLI7d8DAAO7fh4wMOHEio23b9FatzvftK9kaun//Re78/DOskPhcA/k8x6ZNqJOvo0vs0718CW3aAIdTR/YFqJXOpd694c0bAdr4sjAh+SABOB583PCQ4eLziwWUySmrvLAwWFMz1tISsTEjA/bty1JXz2nZMqJjR9/DjGdZcnMh9MtxBj4+0LLlt+kkBwyAHTvkhEptNUye7tgx0NWtXa0u76R2acYMWMVodBATkt5+nCrO2I1jO9t2vhJ9hV4mv/sQe/tHHTvmh4dXE3LTpk99+35q3jxSTc1XX5+pnb/+qpbkcKBnT1i+nF6RywU3N3B1BQsLePcODh5ECwPkuDYgPx/+8x8gOw3Sthwtin46f39wdITu3UFbGyWCgujPznt/+TIcOgSWljV5v/3GsMuqqQIAUru0axcMGlRLlZAbTEg6MA8THmrM1RjsNFiOwQFoNrJjYkLV1B7b21ezMSMDHB3LRo3Kb978mbLyfQ2NyqIiWhUBtzk5cONGTf7Ro6iTzMysyQGAkyeRCQDEyd69oagIzUCOGVNLRpabx48RIXmnauRlkcnTff4m7N4d7t0T8wTJyXD+PJSWwnffIQQAIDsbuS3p960sLnl6IusMXq0xIemtuchzkdJMpdXn6nBW7TaL9aBnT/a7dzWEtLUFFiu/RYs3HTpEqKmlnTpFd4v/3tOzVgOXl6NBFEfHWoLnzlXfrl4NNjYonZ8PhYW1ZACAy4WZM0FPT+i/qVOhuJheCwCN2f7nP7UmPBhaFKCrdhaTp0tNhe+/R0wTffn6QlkZXL8OAwZUC16+DN26ia4koFQWly5dQkDxD33xmcGErAVJTlFOf8f+3eZ3k3twAMrMm7/+Cu/QIfbw4Ro2ZmTAtGmgq5vftm1iu3YRampJYodJsrPRX33atWsXtGhR3SXSirS0gAnJabXE3t66hX5nCQkCBMVaDA6GyZNB4Mokhk934QKMHi3AtMAsa2twdq4uWbYM/QHiv+rOJV9fBFS2+B18mJC1muXMgzMqViqsrSy5BwcgzXAqKu789FPIr7/WYmNqKkyaBLq6BWpqKa1bR6ipJQ4YADExtTyj3bi6Qnk5LQ/N+LdrB0uX0vPLyxFR376l58t+//Qp+p3xvrKSOplYPH0alJUhNVWAFwyfzsEBVq4UUJ0/6/OXrZISPHtWXTJ8uODJ+rpz6cQJ+L//AwahzDAha1qPy63D4ACkmUfr1oWpqGQHBdUi5OvXaKhQV7dEU/PDDz9EqKm96N4ddu2q8YyWys4GDw9aXvXtunWIe9TX0fv3KP/ePfRzJK/4eHj0qDpN/U/qV9bycvTSyDuow9AiZZo/wfzpRo6Eq1eRgtBQiBU5QZWUhGCpqkLCxcXocy5akvBIsru0YwfDl2RMyJpfBBkc4KelP9VRcADIzy+cPDmGdyyHnPMICyMJWTl4cF7z5o/V1B537MghCKGfHKtXI0KePSvg3/79qMtycEBPdeIEWjBQVYXW8QwZUv2cLi7Alvic2RqM+FO6urBzZ3W2XCwyfDoA6NoVXr9Gj7N3b7UDfn7Qvz9kZdHdJN8duFyU7+EBrVvX+vymS/Pdy+ISqczMrNYYL58FKgMTkoICtl7Zqm6jbu9ZZzsh3NzQp0tSUq3uMSMDDY186SFhzJiCFi2iVVQi1NQKxo8HaoCkxkeAvDxEs//8R9S/Fi0QmaOiYMYMOHoUIiJg7VrU5W7bBomJvMrkkPb1BSOjaj2yW2T+dABw+DCsWQP799d8iJ47B506Cd5f5uyMhE+cQB+uOjoSPLiMLpGWNDTA15eJUUzIapQKywqneUybcnjKg7gHTICTWCY+Hq3A9vOjszEjAzUVSciJE4tbtYr5MtD6YeRImDVLzr2ZxE4zqMDlonkUBuOHDHTJQ6SyEkQv0B8zBi02rM/rwQPUmVdWMrGJCVmN0vVn1wk3wvqkNbtKrm90pHouFw0/ODgIYGNGBpotJAmpq1vy449x7dtHqKm9GzgQLUkLDmbSit9Y5vbtulqsI8WDPXkCd+7Q6+3dW/2RmZCAZmv532npFeR6b2YGV5guMsGErIZ+ic8Swo04FcpgAlCKxiKXrVLrcshPR+q/Bw5QhCxVV3/fpk2Emtqrnj0RIRmOIkrhknyrODpCXJx8VUqpbedOel/04QMiIbnG0MIC6vnU6sBAmDeP+bNgQiKs3n54Sx41VyfBAUpLwdoajXxQDKQltmyhCFnRs2dGq1YRampRnTohQhJEQ/mhi/5NlZXJc0WeaFsiSlNT4e+/BZS7u6Np2C1b0CdDfV4FBejrnRzdZWYXExLhVKfBASIWLcqdMAHxisZD6nbZMoqQ3MGDc1u0iFBTi+jYsdTGBg3DREQwa0os1RgQwISEssoyi+MWhBtx69UtuTdp+uPHj1RUopYvF8rGjAwUI8fICBYsgN9/h9GjC1u2jFJVXaCjExUVJXd/sMIGjgAmJNx6dWvgioFGB43qIjjA7TFjQvr2rUpJEUXI2Njq0nv3YMKE4latXigrr/vttyuMRwIa+I8Mu8ccAUxImOU2S9lSeZvfNuaoMZR87ukZrqSUeOqUKDZSL64ZGWh1m65uabt2sT/+uH/o0KNHjzI0hMUaDQJNnZCpeal9lvTRtNeUe3CAypKS4J4972trM2Ujycxp00pVVd+1bXv6p5+2bNnSaH5n+EEYItDUCel2003FSsVo19e1JgxhYyB238HhkarqRzJCB283KDq9eHFZt25prVv/06OHPY6eygDnRibSpAlJBgdQm6X2d6SgsXIZmjo3Nja0Y8dwOzvJuseMDNi+vfKnn7Jbtnyorm46dSqXXH4pgye4qmIh0KQJ+SjxkcZcjZ9X/Cz34ACJixY97NmzMjFRYkKeOsUdPvzTlyXmsydNypE9jKJi/R6bvLdNmpBkcICVZ5ntqWP+W4mJAQODqn/+kZiNGRkQEABaWgUtWjxTUVmupRUjelckc5ewpIIg0HQJSQUHePJerkcXV1WhLcJOTtKwMSMDhRhlsYpatXrdoYPLiBHBCrGWVUF+6wrhZtMl5MXHF8e7jDfeZyzn4AABATBlCtr/KnrwRlhpWhoYGBS2a5fQrt2xgQPxVKRCsEiOTjZRQnK53Hln5hFuhE+EXM9mKyxEWxBdXaVkI8lSW9sCFZXkNm0u9erl5eUlx8bGqho+Ak2UkM9SnxFuhJGbUVYh3+5yWRrt6NHqCKjCOkAm+evXF2hoZP7wQ7CGxv79+2VxB9dVOASaKCH3/LuHcCO2XJfnzHtWeHilnh7abUyybsMGUFWFdesE9JZnzqD9/mfPCijKyIAjRwp69/7YosVjNbVt+Iw3haOUbA43RUKSwQEINyI0/kscftkQpGrfHjbs0S+/oABTGRkomFq3bmgrUJcuKE3rGHV1UYSVSZPo+aTY338X/fxzfvPmT1RUtltZUfpxoikg0BQJWRfBAZ4cPBiupJR84UI1x7y80NBORgba0EgG86Y4+eQJimj8/j2K/vLkiQBOPnpUOnp0fvPmL5WUdk2c2BR+hfgZKQSaIiHnec2bcnjKyQcnKRRkTJR9+hTcvft9ff0ado0di0JlZ2TAtWvw2281+RkZaEZk8WKU4+AgeHYkKal8woSPLVq8bd/+yLBhMvqGqysWAk2OkG8/vO25qOdPjj8lf0yWV1MFz537qGPHwsjIauLdu4dOVqG6xIEDUWgc8jY1FXWMDx+i24cPUZr/hTYjo3LaNPK4yPN9+1YyC44kr2fBer4tAk2OkC5XXJQtlS0P8hyEJFsLZD59+lBVNXLJkhoGzp4NBw7U3O7fj87rJAl5+jSKfk9xdfRoOHOm5vZrftXSpamtW6e3avVvt275+fmyOYhrKxICTYuQZZVlI9eOVLdR//fll3NO5dFSt8ePv9+7N+f9+2pexcZC587o7Lev7ELpzp1R1LOMDGCx6PFUdXVrJKkqu3cntWuX07JleMeOmSkp8nAT61AMBJoWIW+/ut1pTqfha4bLKzhArI9PeIcO8ceO1ZBq61YUiYOiFplYtAi2bkVnYJDDOVRpUhKoqaGIxlQOmfD2jldS+vj99+HKyu9DQhTjp4S9lAcCTYuQcg4OwOHAggXpc+bU0Ck9HR2cGhFRk0MSLDwc5S9bBhs30ovWrUOnkdcmZKm/f+h33+X897/3/ve/E+QxcvJobKyj4SPQhAhJBQd4k8notHfxjefnh4JTvXhRQ6ezZ+lvpLwx/zU0BMSei42FPn1oQzt+27eHtmxZ8t13ca1b27ZpI94TLNFYEGhChDxy64iKlQqxk5BP2+XlgZkZOrmlducml9vrx4+//v774u++e9q2rVmHDvJxGGtRBASaCiE5VRyDPQadbTv7RjA680R827m6gpUVJCfLhYE0Jdxly7L/97+jzZrNaNbsoKureGewRGNBoKkQ8lHiI8KNmOo+Nb9UHrMIb96gk3PIqX/59pDx8ShMq5raw6FD9fT0pkyZ8uBB3Rz+01h+wY3sOZoKIbf6byXciF2Bwk9BZd6wXC4anlm2jNatyeH2/n0wMQF1dfj5561OTsSX6969e8xdw5KKjkCTIGROUY7xEePPp3fIJThAxLZtsb16cR8/lgMDqd41PR2OH0cHCnTpApqacPToxo0bSULe4T/LSdF/dNh/4Qg0CUJefHyRcCPmnp4re3CA4qysEA2NUBMTebLxzRtYtozLYpVraICGBnoZzsnZvHkzScjbt/mF78wAACAASURBVG8Lbz5c0tgQaPyElG9wgLszZz7s3LmYd6qD6uWkS9y6BdOng67uR3X1j82bV2ppwZEjALB+/XqSkDisTmPjnMjnafyElGNwgNSHD8OUlaPXrJFP95iaCocOoV2RuroFvXrlNWuWP2AAGBsj5QBr1qwhCYkHdUT+gBtbYeMn5LoL6wauGLj+8nrZm+72qFH3+/fnpqXJgZAvXqAVdl8OTi4ZMiSvWbPcrl3R5sm9e0k/nb4O6jx69Eh2z7EGRUGgkROysKxwyMohGnM17sfdl7FJnrq7hyspJQmLuyHR+6q/P+oJv7Cx4rffPrZoka2sjDY0GxmhjctfLkdHR7KHjIyMlNFzXF2BEGjkhLzy5ErH2R3HbBzDrmLL0irlhYXBmpr3WSxZ+8bkZNi9mzqetUpbO7d165zWrTn6+qh73FZzAtfixYtJQkZHR8viOa6rWAg0ckJO3TNV2VL5YOBBGVul6MSJ1/365YeHy0TI6Giws6PYCLq6uR065LZoUTFhAmIjQaDj6L5eCxcuJAn54sWLr3n4/40fgcZMyLisuJ6LevZe3FvW4ABZWWi+nvkxjwJfX319EeW+vKZW/3fQoLJ27YpHjKhm48aNvD+3WbNmkYSMj4/nzcfpxo2APAnp5eWl9eUaOnRoQ0Btx9UdKDjAIZmDA+zYATY2tA0ZEneVgYHoE5Ei5IgRKEjk6NHVbCQIeP6cF7Rp06aRhMzMzOTNx+nGjYA8CUkhpaWlRaW/VaKcXU4GBwh8ESiTD8+fw+TJcPOmxAzk7yejotB6dF1dGDsW7UsePLiGjStrHfhTUVFBspEgiIKCApn8x5UVCoFGS0gqOEBpZan0LcLhoMkJeU08ZmTAiROgrY0ievTpg4ZVyU9HgkB7mnmuvLw8ipAcDoenBCcbOQKNlpCr/149ZuuY7Ve2y9SA168jzjx7JofuMSMDbt9GywC6d0cxlA0Mati4ZAnUPpg1LS2NJKSZmZlM/uPKioZA4yRk2qc0oyNGhBshS3CA/OTk9LFjuYcOyYeN0dFgYlLatSsK/airC1u2oIEisofki5rz9u1bkpBz5sxRtF8U9lcmBBonIf98+CfhRvx+7ndZsAkyMQnt2rWcjBbH/0EoUU5CAsyende1a16zZmUjR8KOHahLfP4cHSiwYAFUVdH8jIiIIAnp6OhIKxJ1W1IiqlSKsqIikOhwERHy+fmwZ48ULgitIpEtuVsX6pasBY2QkJwqzqxTswg34kr0FanheXfrVpiS0vOtW+XQPaalwYoVRf375zVrlte7NwpYXlZW7VhmJgpFx3cFBASQhNy6dStfoZCMqiq0SF2OV0UF2nfCfNJFrHxQELluXg4+SmFLjtbl8ABCVTRCQj5KkDU4ALeqKuiXX0IGD5YDGzMyYO/eshEj8po3z+nYEaytIUv8AXjnzp0jCXn48GGhTefoCHp6tf61agU+8jvu0tkZXFyEWucvECjv7w8fPtTIzp+Pgp7IfvHbohkCAH5b/DmyeyJvDY2QkLIHB4jcvTtcSSn177/lQMgLF9jjxn1s2TK7fXuusTG8esWkBd3c3EhCnjt3jok8ktm7F1auBLZMKwRrbH3eifLjj5CbW5MjOiVQnstFSp4+rakaEYGCuMt48dviNwSABq5ptvhzZPSkDqo3NkLmFOVM2jsJBQdIfiIdXCW5uSFduz4gz66S6EORXzg4mKunl9u2bU6rVmxdXTTKyuzaunUrSciAgABmNQBevmQqyURu0yY04MT8Eij/8iW0aQO0aZveveGNbGE4+W0JNAQA/Lb4c5g/Y71INjZCnnlwRtVaddL2SVIHBwiePfuhunrx06eydo8vXoCp6UdV1Y8tWpSNGYMOpWN8UVs9wsPDGVeSq+CAAWjkifklUP7YMTSeTLtmzIBVq2h5kt3y2xJoCAAdL0+zxZ8jme06l25UhORyuZO2TVKxUvEK8ZIOufLExIiOHaOWL5eVjUlJYGsLv/xS8eOPhYMHo0kOvqFUER5aWFiQPWRiYqIAMS4X3NzA1bX6+PSDB2HDBvRPXld+Pgr3/G/t409EGOWX9/cHR0c046qtjRJBQTWu7dqFjgYTfV2+jLZuW/Ksefztt+p+lWZLhCEA4LfFnyPak3ovbVSEfJbyrNv8bj8t/SmrUPzAiWCot2wpt7GpSkmRiZDp6Whxz+jRaLXq8OGwaBFIMiGRn59PspEgiNJSQcuMyBNgARAne/eGoiKwt4cxYwQ/kRS5jx8jQtKGf0UYFSgPgAjJHzLP0xO++47+HsvrZHIynD8PpaVIrKgIlWRnI3/S01FaoC2BhgCA3xZ/Dq/pBpBuVIRc67NWaabSguMLpAQ2IgItoKHOcuT/JmSYc+gQjBuHojkOGID+zJO/JMY+vXnzhiTkrFmzBFeiRnpWr0ar3gEgPx8KC+nCXC7MnFlrGJY2Kjt1KhQX02sBoIW7//kPfcJDhFGB8qmp8P33iFe069IlpFzEcJGvL5oWun4doUdely+jtU3kxW9LmCEA4LfFn1Ott6H8r/EQkgwO0Nm2s5TBASor0WbFzZtl6hszMuDyZdDRQdEce/ZE2zuePZO0qYODg0lCrhY7Ka+lhTaFyf26dQtxJiFBsGJ+owLlL1xA7wj8l68vUp6dzV9SK8faGpydq3OWLUN/WciL35YwQwDAb4s/p5bVb3/TeAhJBQeo5FRKg6uvLwqrERMjEyFDQ1Efq6mJCKmvD//8I4UnPj4+JCFdRR8iUF4OLVrw7mmWwpbgKk+fIs7QXllJUYFGBco7OKBpGP7rxAn4v/+Digr+kpqcz9+rSko1f8uGD69ZUcBvS5ghALSUn2aLP6fGaoNINR5CksEBXAOkOgkjJwdMTVH7MXwpFSj26hWYm5d0744OgdTRAXd36Vp43759JCEvXrwoWAMZd+fePfSrJa/4eOCPhSX1K2t5OXrbpA3qiDAqUH7kSLh6FXkXGooOq6WuHTtq3j+pTFoiKQn9rSGHwYqL0cckFceE35YwQwBooJh61yVN8OfQTH/r20ZCyLisuGHrhvV16Ps+tzpIlETAljk7w6xZMp2c8/nUnQUL8r9EcyweMgTWrxc1biHSOQcHB5KQoaGhAgRPnIAffkA/1vXrYciQagEXF7ktCSA16urCzp011sUapckDQNeu8Po18uprHL1qbWZmtYZP/fygf3/66qWCAmjXrnoHjIcHtG5dC0yaLWGGANDxZLxDtQJzah6yQaQaCSHdg90JN2LlJUHvSOJwfuvnF6GikuvtLVP3uHFjyeDBKJpjt25o0Rb/EIs4N8hyNps9depUkpBpaWkCKkVFoem1o0fRSpS1a9HI/rZtIHB2REBlxlm+vugDmLrEGqXJA8Dhw2ioef9++PSJUoMSGhro0466zp1D21/4V/w5O6PqJ06g3eE6OpQ4StBsCTPEb0tgTi3V3/6mMRCynF1ucdyCcCNuxtyUFNEqNvtO//4hI0fKxMZjxyp+/bU6mqO5uSzLNd+9e0eycfr06dzamyQlfTSZ5LlcNI8iYiyUpp2h/IMHqOesrP2RX1kJf/5J01dzO2YMitPHe0ltS6B1Xs0NIN0YCHnnzR3CjTA7ZiZFcICwzZvDlJWzAgOlJ6S/P0db+2OrVjlt2lQZGKCJMhmuu3fvkoR0cnKSQY08qt6+LdliHSbyZmZwhW8LzpMnQDtQaO/e6s/OhARo2ZL+QguAFiGKXUjEb4s/Rx44yVdHYyDk2strCTfiUNAhSaEpTE+/37nzQzMz6dkYHg5TpuT++GNuy5YV2tpozkO269SpUyQh3dzcZNMkj9qOjugMduaXaPnAQJg3T4CynTtr9ZkfPiASkt/PFhbg7S2gCgBaACTCN35b/DmC9X7jXIUnpCzBAe5Mnx6qoVH66pWUhIyNhZkz8zp3/ti8efHIkXDggOyNSZ1C5+/vL7s2WTWUlUm2Ik+EfEEB+uLlXz+Ymgp//033090dza9u2QJ+fvQi6l4iW8KsU9oaTELhCVkdHOC8xMEBku/dC1NWfrZxo5RsTElB8a+GD2d36JDfvz+ac6N9Gknexlwul1rF+kbGLRGSW8c1GgICik1IThVHx1ln6NqhV57yfZmIQ/f2sGEhgwZJf3LOtm1o2ENNDc092NpCXp44g+LLk5KSyPfVadOmVcpMb/H2sETDQ0CxCfko4VEXuy6Dlg/KL82XDNuQkI+jRqX5+krZPXp5wYQJKJpj374ocIawVWaS+QSBgYEkIVfRNg1JqAeLKy4Cik3IxScXK81UWnlWwunHsjK0JtvFRUo23ryJojl264Z2MxgaVg8/yOMn4OrqOnTo0MmTJ5+qixWq8vAQ66hrBBSYkLlFuf0d+3ed11Xi4ADe3jB1KhpYF7gCTnTmkydoxrxPH9Q9TpokYEZbhhazt7fX19fX09MTvEZHBs24qqIgoMCE9A71VrVWnbh1omTBATIz0SLyM2ekYWNcHFhbF2tqclVVYfx4tEpGfnP3eXl5RkZG5CtrLvMZeUX5oWE/mSGgqITkcrl62/VUrFRO3ZNw/5GzM9pmlZoqMSFTU2HZssKffspr1qygXz80D1ZezgxkRlLUrquFCxcyqoCFGiMCikrIZynPui/oLnFwgCdP0NrIO3ckZmNGBuzeXTZ8OIrm2KkTWomekyPf38PBgwfJ7tHDw0O+mrE2BUJAUQm57sI6pZlK84/NZ441u6wsesSI/CVLpGHjuXNsLS0UzfHHH7kmJrLGTfviNJvNdnV1paLm2NrakoR8xL+RivlDYkkFR0AhCVlYVjjVfeqYrWNC3oYwx//B8uWPVFVzpYjQcecOd9KkmmiOtIWXzD3gkSwpKVmxYoWBgQF5YnlKSgrJRmNj4yIykAyPME42HQQUkpD+z/0JN8LqpBXz4AB5iYmhHTuGzZ4tcff47BlMnfpRRQVFcxw7FrykjGfH+5PKzs6eO3euqalpwtcJTH9/f5KQ335NOa+jOF3vCCgkIZdeWEq4EZ73PZnDddvQMLRbt4r4eMkImZgItrb53bvnNWtWOGQIbN0q+7BqYmLi9OnTbW1ts3jOFNi0aRNJSAlClTN/eCypOAgoHiHjs+I/ByYn3AjmwQHi/f3DlJRidu2SjI3p6SjM7ujRHGXl/D590MpVSaI5CvwNREVFGRgYLF++vJgn3FtxcbGJiQlJyLdv3wqsiDObCAKKR0iPYA/CjXDyZbpdEJ2cM2hQyNChkrExIwNFPR03DgXIIaM5ZmbK+JuIiopisVguLi7s2idwhISEkGycM2fOt9yULOPj4eryQEDBCEkFB/g3pnZcbeFYRGzbFq6snOHvLxkhL11CkSM0NKqjOb54IdwC05Ly8vKrZNyn2jV2795NEhJPeNQGpineKRghg14H6ezSkSA4QHFx7PDhoVOnSsbG+/drRXNkfuKN5D+hyspKc3NzkpDkiKvkOnCNxoOAghHS5oiNsqXyNr9tTFvgxAkwM+MmJEhAyJgYFK3sp59Q6PGJE1E4qbq8qMOSLSwsaK+ydWkW626gCCgSIdM+pfV16Ktpr/k64zUjOJOT0ZlqFy9KwMb372HevKI+fapUVGDsWLRfnnaaGiPDEghR76sH5BFwQALDWLRBIqBIhHS/7a5ipULsYnxu4YYN6BSa9HSmhExPhw0bir9Ec8zT1IQFC6SO5ggASUlJz8SdI1BSUmJqakq+rz55IuWBlg3yd4WdkhIBhSEkp4ozbvM4tVlqvo95onqKeOqHD9F34IMHTNmYkQEeHtXRHFVUwNwcUlJEqBddFB0dbWhouH79etFiQUFBJBtnz55dxR9vRnRlXNoYEVAYQoYlhkkQHKCiAoXV2LpVAjZeu1YdzbFt2ypDQ4iKkrq5b926xWKxnJ2dxYbhoEJaeXpKsMhBasdwxYaPgMIQkgwO4OTNaPoxZfdurrExWgIuercxVRoWBoaGNdEc+WOHMm7Jc+fOaWtrHz9+XOyMYk5OjrGxMdlDxsfHM7aABRszAopByNyi3AHLBnSd1zXqvfiOK+vly4eqqk+Z7+p48wYsLD526oSiOY4aBQcPStfgVVVV+/bt09HRETjZyK+TOuVq0aJF/KU4p2kioBiE/Cvyr35L+7GcWUyCA9yeOPF+z57spCRG3WNyMvz+e2GfPnnff4+iOa5eLV00x/Ly8jVr1ujr6z98+JDJL4nD4VD7rRgSmIlaLKPoCCgAIblc7nzv+YQbcT78vFi4X1+4EN6hQ+zhw4zYmJGBvjPHjKlSVc3X1IS5c9FRxFJdVVVVu3fvZh5MNSwsjHxZNTU1LZT2ZB6pPMWVGjQCCkDI56nPCTfCyM0oqzBLNJacioo7/fqF/PorUzaePImiOXbqhKI5mpnJ/wwp4e5u2bKFJKSYU1mFa8AljRIBBSDkvpv7CDdi09VNYhvg4dq1YSoq2UFBjAgZGAi6uugwJjKaYz3u08/MzKTiWTHvVMU+PhZoBAg0dEIWlReZHjUl3Ij7cfdFw52fnPygU6dHlpaM2BgZiaI59u5dHc1R2FnFok1KW3rs2DGye1y6dKm0OnC9xolAQyckGRzA0tNSbHCAkOnTQ7t2LWcSbTUuDqysYNAgtLVqwgTYs0eKbcfvySO+Jf9VFBYWmpmZkYS8ffu25ApwjcaMQEMnJBkc4MT9E2IaIT6eo6+f4eEhvntMTYWlS4v69+coK8Po0bB8OVRUiFFeu7iqqsrV1VVPT0+66KkXL14k2WhjY4NXk9eGFt9BgyZkfFZ8/2X9f/vjNzHBAbhccHICBwfxbMzIgJ07S79Ec8zt3Blmz5Y0mmN5efn69ev19PQePHggxc+noqJi1qxZJCH/5j+GTQqNuErjQqBBE3LXtV3KlsozXGeIwfzOHbRsNTxcPCG9vSvHjq2O5jhtGkgYL+PTp0/29vYmJiavXr0S45KQYuo4HXNzc94oHkLEcXaTQ6DhErKcXT5y7Uh1G/WAFwGimqW0FKytUVR/ah2csERQUJWubnU0x0mTIDhYlFq+spSUlJkzZ1pbW6elpfEVMspgs9l2dnZk93jy5ElGdbBQE0Og4RIy6HVQpzmdhq0eVlpZKqpRvLzA1BSdbi2Mh2T+06comqOyMormqKWFzvaQ5Hr58qWRkdHixYvzpV05AAABAQEkG01NTaX7/pTEZSyrkAg0XEKSwQG2/r1VBK7c1FQ0e3HunBg2JibCnDmfunVD0Rx/+QW2bZN0WPXQoUObNm0ql+Ewj8rKSmqt3IkT4saoRDwzLmrUCDRQQqbloeAAPRb2EB0c4M7YsYkTJ0JamihCpqWBk1PxwIF5zZp97NULliyBUpFdrqD2rqqqErt7Q1C9mjwqFPL06dPz5HHcco1qnGpECDRQQjIJDvDc0zNcSSnx1ClRbMzIgAMHQEuL27FjQdeuaPrxw4f6b76ysrLZs2eT76te8oh9Xv+PgC3WDwLyJKSXl5fWl2vo0KGyeM+p4ozfPF5tltpfEX8J01NZUhLcs+d9bW0xbPzrr+pojr16gYkJvHwpTGGd5vv4+LBYLIIgzMzMZPkKrVMnsfKGgIA8CUk9j5aWFpWWIhGWGGZw0GDizon5pUL3Xtx3cAhTU8sLDRVFyJAQdPicpiZ06QL6+vAv01Cu8p2vz83NNTMzGzNmjJ6eno+PjxSA4CpNB4GGSEhnf2fCjdgZsFNYM+TGxoaqqYXb2Yli48uXaPS1Xz8UzZHFAsbjKGlpadbW1vfvi1k6K8w3/nxXV1fyZdXW1laWYSF+zTin8SHQ4AiZW5Rr4m5CuBEiggPcnjTpQY8elYmJQgmZlISOSf7lF1BTQ9EcN20CZiGkXr16ZWJiYm9v/+nTJ7k0dnx8PLWx4448zrGTi1dYSYNFoMER0jfSl3AjbP+0reJWCUTtrZ9fuJLS6337hLIxPR3WrSv++Wd2hw4wbBiKBMnsxMX79+/r6emtX79exn6ssLCQXDzA5XJXrVpFdo/Lly+XcZxWIBo4s5Eh0LAIiYIDnEHBAc6FnxMMdFVVrqXlEx0doWzMyIAjR8pHj/7YokWOqirMmIEmRRhcly9f1tHRcXV1lTEc482bN42NjdetWwcA//77L8lGIyOjmJgYBl5gkaaOQMMipPjgADduwJQpEB0tlJBXrtSK5hgdLbaFuVyuu7u7trb2hQsXxAqLEEhLS1uxYoWOjs6hQ4dKSko+ffo0c+ZMkpA4LIAI3HARLwINi5B/XP6DtYe18cpGXhdr0oWFqMdzdRXKxkePuAYGue3b57ZsWamjA9ev19QVnrp3756urq4sH3hsNtvb23vSpEl2dnZUBIB9+/aRbLS0tMRTHcLhxyW1EGhAhCwqLxqyckhn284hb0Nq+UjdeHiAhQW8eyeYkGQ0R3X1j82bl4weDYcPU/XEJpKTk8XKCBN48eKFjY2Nvr7+hQsXOF8PAomOjibZSBAE3oUsDDqcz49AAyLktafXOs7u+NuG3wQHB0hMRC+rly4JZmNyMtjbF/TqldesWf6AAbB2LdQ+FJX/yeWVs2PHjjVr1mTyHOdaUlIyd+5ckpBr167FYznygrop6GlAhDTdZ6psqewa6CoY9zVr0KHiwk7O2by5bOjQvGbNcrt2RRMeMuzJEGxdeC7/eQHUxKOpqWmKDAeECLeJSxotAg2FkPFZ8T0X9ey9uLfA4ACvjh4tGDsWHj0S3D2eOAHjx4O6epGGBkyfDtJGu5FLI1MBVwmCuCLDkQRycQYrUTgEGgohRQQHKPv0Kbh79weTJwtm440baCFO167Qowd6pw0PF90GV69e9fVldn4WnyIOhyN6VV1+fr61tTX5srpu3Tr8ssoHIc4Qg0CDIGQFu0JEcIDguXMfqqsXRkYKIOTjx+hIViqao0imcbncY8eOaWtrnzsnZJJTJFYxMTFz5849I3xnM5fL3bx5M8lGc3PzrCwxYZ1FWsOFTRSBBkFIKjhASUUJrR0ynz59qKoaKTCA1du3MHNmTTTHfftodXlvKysrnZ2dWSyWFGOexcXFrq6u2traK1euzMjI4FXLm/b29qZGVm/dusVbhNMYAYYINAhCLju/rOeinn/8/Qe/07fHj7/fpw/n/Xt695iSgrYajxgBqqoomqOTk4hojoWFhY6OjoaGhtEM1gnQfAgODjY1NTUxMQkKCqIV8d6GhYVRa1b379/PW4TTGAHmCHx7QqblpRkdMSLciFfp9FBuMd7e4R06xB8/TmdjRga4uJQOHVrx448weDDMmQMfPwp75g8fPtjY2JibmyclJQmTEZifmZm5Zs0abW3tvXv3ij4PJy0tzcLCguwely5dWiFhoFeB1nFm00Tg2xPy9MPThBux6Bz9jER2WdndPn1CtLQEsPHMmepojh06wLRpIPy006KiIlNT03nz5kkaVIrL5VpbW9vY2Dx//lz0L6O0tPT3338n2Thz5kzeCUnRFXEpRoAfgW9MSE4VZ/ap2YQb4RftR3MuYc+eMDW13OBgOiFv3apisXLbtMlp1Yqjrw/iNi4GBQWVlNA/TWm2BN6+f/9e9JgqWWvnzp0kG42MjKJkOAhdoA84s6kh8I0JGf4unHAjTNxN6MEB8vJg+vQy/mWr0dFgYlIdzXHcODh79ts22N9//00N5Fys3xN7vu2DY+t1hMA3JiQZHGDHjR30x3N1RQGpkpNrdY8JCTB7dl7Xriia49ChsGOHpNEc6VZku3/27JmxsTFJyG3btuFZR9ngxLURAt+SkB+LP5LBASKTImu1xps3YGgI/v612JiWBitWFPbvn9esWV7v3rB0KZSV1aol7U1WVtamTZvi4uIkUpCSkmJpaUmy0d7eXrq3YoksChMuLS319PQUVsqfL5F8cXHxX38JDTXGr1xsDnPrAk0LzBRrVIEEviUhzz08131B9+mHp9cKDsDlwrJl6B8tEvnevZWjR+c1b56jro7ODhA07V5cXHz16lXm6FdVVV26dMnAwMDa2vr169fMK2ZmZs6ZM4dko5mZmSybRZgbFSjJZrM3bNiQnp4usJQ/U1J5AIiOjr527Rq/KilyJLUu0LTATCmcaZhVvhkhuVyu3jY9FSuVk/dqn3Jx8ybqHqOiahHywgUUzbFz55LOnbkmJiDorJusrCxbW9vp06czDIcTFxe3YMECFovl5eXFv0BcRGvl5ubOmzePZKOJiUlERIQIYbLo2bNndTQ5efbsWYki2QmUDwsLEx27+cCBA3JZeMRvXTrT8vJHbMPVv8A3I+SLtBfdF3Tv59DvQ0FN5OKS7GyOhQXQ4uUEB6Mgjj16oAWrkyeDoENOExISPm+tmDt3bnZ2tlgQS0tL3d3dJ06cuHTpUua7MTIzMyMjIz98+LBo0SKSjUZGRsEMTuwhz9hxcnIS65ikAtnZ2SYmJgUFBQwrCpTncrkmJiYJCQkilLx582b37t0iBJgU8VuX2rRc/GHic/3LfDNCbri4QWmm0ryj83if+c6MGZE9egBvOLkXL9BMY79+0KkTWkQu6NCoyMhIAwODFStWMPmQKyoqIifxAwJEHqrF41ZcXNzPP//cuXPnXr16/fDDD3379p0yZQpBEIGBgTxSQpMBAQF//PGHra2tUAlpC06fPr1xo5DoCoJ0CpRPSkoyMjISG0nIxsaG+R8vQcaB37ospmX3R6CT3zzz2xBSYHCAlAcPHikrR69ZU/OympQEtrbV0Rw/B1/esoU/mmNAQACLxdqxYweTOUMSbn9/f4avtQBQUFDQpUuXYcOGsb5cOjo6nTp16tOnz+XLl5k0Xk5OTnBw8Pnz542MjJjISyQzb948id5XBcr7+/uvWbNGrF0XFxcZzwjity6Ladn9EfvI30Tg2xBSYHCA26NG3e/fn0udnJOeDqtXo3WqqqowfDgsWgR88/ve3t4TJkyo09Mydu/e3bdvXxaLNW6c2a+/zmWxdHV0dNq2bcukNwaAa9eucbncf//9CfQzEQAAFC9JREFUl8VilclpWJj8oRQXF7NYrMjIWgPUXC736tWrly9f3r59e2Zmpp+fn9eXCwD45cPCwtzd3a2srFauXOnu7i56oe/Fixfnz58v+jf64MEDPz+/HTtqJrEcHR3JfpVmXXbTTPwR7W3DLP02hCSDAxwIOECB8vTIkXAlpaSzZ2u6x0OHykeNKmvfHgYMAEtLFCuA7woMDLxx4wZftjwzCMLop59maWqeVlF5pKISNmqUPYvF6t27d7i4jZcA8PLlS3IANioqisViMR8LZfIAsbGxLBbrbe1DoAMCAj5+WdZ7+fJlGxub0tLSgwcPOjo6AoBAeQCwsrISuzyQPNxST09PxJttVlbWnTt3ysvL9fT0Sr+cL5afn89ischFiwKty2I6ICBAtD9MMGyAMt+AkPFZ8b1+79V7ce+k3OrV3uWFhcE9etxnsWrYePkyZ/z4jz/8kNO2LZcg4NkzKbArLy/38fFh/ipLM1FcDFevQr9+99u2vaeiEqaiEqahcW3cOFMWi9WtW7f34uISsNnsu3fvkjqTkpJYLNaLFy9oJgCAy+W6uLisFX5t2bJFYNcqkOTUlhRPT889e/aQHSPZmQuUz87O1tfXpwWGZrPZzs7ONFdDQkJYLJaIAaSQkJCKioqwsLB586rHBR48eGBlZUXq4bcuo2mx/tD8V5Tbb0BIj2AP/QP6C70WUhiF2Ns/6tgxPzy8mpChoSiaY7t2uT/8UDlxIvzzDyXJPBEeHj5jxgyCIGJjY5nXIiXfvwd3dxQMRE+vomPHx99/f0NT04vsG1ks1vDhw/v37y9WZ2BgoIeHh+eXy93dncViMRmSFauWEuD/iVNFnz99ly9fThtzEih/9+5dBwcH3ooJCQlXr17V1dXlzQQAkgBi41nu3Lnz7Nf1jB4eHi4uLqQefusymmboD+0pGv5tfROygl1hcdyCcCP+jak+iyrr5cuHqqoR9vbVbHz1CszNP3bsiKI5/vorYoaE18ePH7du3TphwgRnZ2fR02s0xRwOhIbCnDkZvXu/GTnyw8SJJZqaYUOGHOzZ89f27dv//PPPI0eO7NevX6dOncSGIc/OzuZdaI4mXfX0GI4D0bwSdpuQkMD/ykoKV1ZWGhgYpKam8tYVKH/kyJHjx4/zipHpSZMm0TJv3Lihq6sr+nWDy+VOmzYtMTGRrPv7779TKwr4rctomok/tEdQiNv6JuTd2Luftz6aHTOjggNUbd+erK3NTkpChPy8eHXBgvyePVE0x4EDYf16+Brp9PPXTnx8vOj1olwu99q1a1OmTJk5cyaT+XqqhfLzwdu7XFv7vYZGtJLSQ03NGH392PHjtxsaTiUIwsjI6I8//pg/f/6kSZP++OMPJiS/dOkSpZxMmJubC1zgJvUra2Vlpb6+Pm1Q58OX42ifP38+bdo00m56evqrL+soBMovWbLk4cOHAPA5QAnvrAY/IX18fKj3T9qjUbcfPnwwMDAg26isrExPTy/+6844fusymmbiD+WYAiXqm5Dr/NYRbsTBoIPVGD17hub6b96s7h43biwZPBhFc+zWDebPh8JCCsqbN2+yWKybN29SObTEhw8fFi9ezGKxjh8/Tvsookny3r59Cxs35v38c7yqariqavigQfFr13708npkYmJCzv5PnTpV0lfNu3fv8p9mt2DBgp07hR6wx+sS8/SaNWt4jz+4ceOGoaEhl8s9derUwoXVXwQ+Pj5U+GaaPABYWlomJydzOBxa4C9+Qjo7O1PDp6GhoXZ2dvxTRyUlJcbGxiQhr1+/ThAE7yAQzbp0pilweP2hMhtBol4Jmf4pvVZwAA4HhVpdu7aajceOVWlp5bVoka2iAubmqLf8enl7e2tra584cUJED1lSUrJp0ybqfelrVcH/r6yEO3dg+XIYPTpbSelh585Pxo9//+ef5Xl54OPjQ1KRIAgLCwsmI5CUjcTExHXr1unq6jo6OlJbotPT0/fv36+vr29qanrs2DFyBJKqIksiJCRk06ZNlIa4uDgXFxd/f/83b96cPHny4sWL586d4w0CRJMHgCtXrnh6el66dKmo9gFh/IScOXNmSEh1RPmgoCALCwtqyIpyAADOnj3r6el548aN9evXr1y5kreIZl0605RCXn+ozEaQqFdC0oMDXL+OYsY9e4YI6e9PRnMs79SpysAAHj8mweVwOHv37p04ceJ1Zgd1iG2SnBw4cwatTicI9G/yZPasWRkhIVwOB0pLS6kDOQiCsLW1FTuUKtZcnQpwuVxHR0cRI58068zlaYR8+fKlpaUl7wckm80W8bYCAI6OjrQNogytizVNzifR/KE9qeLe1h8hOVUco/1Gk/ZNuvzkyxqX/HzUDbq5ITaGh6OQqr16QefOoKcHXxfBlJaWrl69Wl9fPywsTHaInz9HOyhNTKqpaGqKjv/4OgCBPlAXLFhA9Y0ODg5UFye76brT8OTJE4kW64iVT09PDwwMZLFYgYGB1LDQ54B9oaGhvE8RFxf39OlT3hwA8PX1JT9E09PTDQ0N+d9pRVtnaBoA+P2heaK4t/VHyPB34V3sugxaMehTyZfDiQ8fRkEck5IgNhYlBg6Ejh1BWxsOVK8WyM3NnT9//rRp0/jnLbhcLvPdUmVlcP06x9g4tUePl3p6FQSBjhrw86v5PuVyuX5+ftRHI0EQmzdvluOLZV3/ONzd3cnzYRkaEi3/Obos+V1AJR4/fsy/VeXChQu8HSYA5OXlGRoakuPP27dvFxZuU4R1yiKVEGhaYCbDZ2/4YvVHSAcvB6WZSivOrACAd7duJfTtW+nrCykp6DNy+HC0Pu7XX2HlSqisJFGLioqytbXl/QQi89+/f7906VJdXV2xPVhaGri6Fo8c+U5dPVJFJaxPn9gVKwojImqFGcjLy6OiGxMEYWJicunSJRFfqg2wRSsqKiRaPCiRfElJycmTJ2mAZGdn849akesEAwMDz5w5Q+tOeUFjbl2gaYGZvPoVPV1PhPxY/HHAsgFd53WNTIrkVlUFDRkSMmQIelndtg3GjAE1NRgyBK0jz8vjBZR3jA4AKisrvby8WCyWvb29iA3+XC76Al20KKtv31gVlbCOHR+PHPlu//4i/pOUnzx5MmvWLOo1dd68ebSVaLzO4DRGoB4QqCdCnn90XtVaVecPnSpu1eNdu8KVlNL8/MDLq3LMmJL27bl9+qB1MSK35EVHR1tbWxsYGFy+fJlGVAqmoiK4cgVNl/TrF6ek9LB79xdGRqnXrnH4F3VzOJxTp05RoY0JgtizZw/D9eKUOZzACMgdgfogJJfL1d+uTwYHKMnJudelywOCgH//RdEcW7fOad0aRXOsPWbA+5z5+fk7duyYMGHCxo0bhe0/fvcOjhwBU9PqARtt7YLly3OELYCNiYlZsmQJ1TGamZkJ++DhdQOnMQL1gEB9EJI3OEDw7NkP1dVLAgPByChXSeljixbl48eDj09VVZWwOBrR0dHm5uYPHjzgh4Nc7LZmTTUPCQKFqjt9GoSFDcjNzd27dy9FRYIgli1bJtGICL8POAcjIEcE6oOQG//aiIIDHJuX/vjxIxWVZ0uWgLV1Xpcuec2aFQ0bBrt2lZWWrlu3jlqIzP94tAG9z9Ncnz7BmTPlEya879cvjpxRXL4cgoKEHvDBZrMvXbpkZmZGsdHY2PjkyZP8mvmt4xyMQL0hUOeELC4vnrRnUl+Hvvdi793+7bf7/fqBo2PhTz+haI59+oCjY15m5sKFC01MTBjOZMTGwvr1eYMG1Sx22727SvSOjqioqIULF1JUJAhi9erVDNf01FtLYEMYgfqIy/rP838IN8LS07LwblBMt245s2eXDR+Oojl26gSzZ6c+fTpz5kxra2tq866wZagVFXDrFtfMLE1TM0ZJ6aGGRvSECe/PnCn/9GVSU1hbZmZmbtu2jZeKs2fPFrjmS5gGnI8RqE8E6ryHdLzoSLgRJ+8eRfPxVlZcbe2PP/yQ/eOPXBOT2KtXCYJYvHgxucuusLBwz549NjY2tNfI7Gz480+YObOqU6coZeVHvXu/sbHJCA3l3QciALHMzEx3d/dp06ZRbDQxMfHy8lKgGX8BT4WzGjsCdUvIhOwEwo0g3Ijsk0fQKhwdHejevVJdna2r++zAgUmTJm3evJnsEm/dumViYmJqanrv3j0K82fPwMUFjI2rx2zGjMl0ccl/944qF5xITEzcs2cPFeSfJOSmTZvw4I1gvHBuHSOwaNEial3+7du37ezsRBisW0IevXeUcCM2nVyEYh+PHElFcyz18DAwMDhy5AiXy01PT3dyctLW1j548GBxcTEAOiLgn3/QAh5ytIYg0NTilStQe0OCgIf6HCNjy5YtVJdIJj7vY3z06JEAaZyFEagXBDIyMqZOncpms0tKSiZMmCBiTUvdfkNWsCtmnJjx+QMybuls6NsXnayqpgbjxsHWrcDlZmZmstnsc+fO6enpzZ07lxzRSUuD/fuLRoxIHDUqiyDAyAj++AMtu+FyRSH3eT9+WFiYk5MTjYpLliy5e/cutRtQlApchhGoSwS8vLxOnDhx8ODBzZs3i7ZThz0kGRzAabNeVa9eaO24qio6gfz336lojt7e3np6el+WKXMiImDhwg99+sQqKz9SV48cOzbtxAmBgeZqPc6nT5/8/Pzs7e1pVFy1apVEEQNqKcU3GAF5I8DhcKZPnz58+HCxC7DrkJBz3Odozu8e+1MX6NYN7eQgozlmZlIPW1JSEheXefFipa5ucteuz8jFbsbGqf7+Aha7UbUAgMPhREREuLi48G7RIDm5detWsQFveFXhNEagHhDgcDh2dnYsFosM0inCYl0RMv1Tel+HvjuHtc1r9n1RmzZcTU30AsoTBzExEW1HnDjxk5pahIpK2IABcU5OuaKPD2ez2VFRUYcOHaLOgaM6RhMTk3379jXw/cQimgEXNW4EvLy8Lly4cP78+W/2ynrszjHW5B8zfvhfQfPmOS1bvtXUZH/Z8s/hoDPIV62qHrCZPJk9dmzSsWOlOTlCW6SgoODevXuurq5kWEeKhGRi/vz5Fy9ezBFRX6hiXIARqA8EMjMzzczMOF+uKVOm1N+gDpfL/euvvwwMTNv/2KXPFOXIDv8r/P5/H5s1e9qhw5lff3V1Pe3jA7Nn14ydLl+OAtt83f9YC5rS0tJnz555e3uvWLGCxkDy1szMbP/+/QJDD9dShG8wAt8agUWLFlHbR0NCQupp2qOkpERLS7dHjykjR17/Te/i+R7Ked//36f//vdFu3bnug//qc9xTc1nurplBIEOs9q/H2qHwAc2m/3u3bs7d+54eHgsXbqUd2MULyHNzMz27dv36NGjioqKb40zto8RkAMCZ86c4R31kNs3pJXV3P7916C5CoK7b/CktFYtS7/7/vn3Xby+H99TNZhc7GZsnPfXX5CfD1lZWS9fvrxz546Pj8+uXbuWLFlCm8fnJSFBEPPmzXN3d4+IiMA8lMNPAKtoSAjExMRMnDiR4qR8CJmamqqq2sfQsJIgYNewE0+V2pf977/vmmlcbWHe7b/nlJQeDh9+a/bs44sXL7Wzs6ORTditlZXV9u3bb9y4QS1zbUgwYl8wAnJDgJeT8iGkr69v//52BAGzdTPuqQwr+u673O9b3GxO6ClHtW9/dPBgI2Gs482fPn368uXLjx49evfuXf5QOnJ7eqwII9DwEKA4+R8vLy8tma++fft2726L1rjpJIQo/ZLVvHlI20Ere10xMIDOnc1bt27dge9SU1Pr0qWLpqZmv379hgwZMmrUKJm9kF7B0KFDpa/8LWpih+sa9fpHeOHChUuWLJFPD/n69evOnYeSS0/3DL1wudu8XcN8v9xylZR6Hzx48OrVq3fu3Hny5ElMTExWVhYtitk3/4Ol9fl4ZoW6sMN13Vz1iTCbzd6xY4eZmVlaWpp8CAkAWlq6Q4eeopaDk4lffvFgsabUNXay65cojKLs5mTXgB2WHUPRGuoN4bS0NDMzsx07dpC7DuVGyPT09G7d+g0cuF5XN5UggMVKHjBglabmgKysLNFPjksxAk0ZgTNnzlDH7Mp5t0d+fr6T0/oePfp///0PPXoMWLt2M/NjJ5pyk+BnxwhQCMith6Q0fnl9VbBPMl7ncRoj8A0RYETIsjIURMPODi2ymT8fxVksLRXlc31+EIvyA5dhBBQNAfGErKhAJ26cOoWO4WCz0Xb+mBjYtAklhF2YkMKQwfkYAdEIiCfkpUvg60tXcusWnDtHz6TuMSEpKHACIyARAuIJ6egIubl0nVlZsGQJPZO6x4SkoMAJjIBECIgn5PTpAhRWVoKZmYB8MgsTUig0uAAjIBIBRoRks+k6KiowIemY4HuMgOwIiCekoyPwb8fPzsavrLKDjzVgBOgIiCfklSvg40OvFhyMB3XomOB7jIDsCIgnJIcD69eDnx8a2uFwULTiyEgULlXEVCT+hpS9YbCGpomAeEICoDPezp9HSwLIhQF//kmFVhUMGiakYFxwLkZAHAKMCClOCb0cE5KOCL7HCDBDABOSGU5YCiNQLwhgQtYLzNgIRoAZApiQzHDCUhiBekEAE7JeYMZGMALMEMCEZIYTlsII1AsCmJD1AjM2ghFghgAmJDOcsBRGoF4QwISsF5ixEYwAMwQwIZnhhKUwAvWCACZkvcCMjWAEmCGACckMJyyFEagXBDAh6wVmbAQjwAwBTEhmOGEpjEC9IIAJWS8wYyMYAWYIYEIywwlLYQTqBQFMyHqBGRvBCDBDABOSGU5YCiNQLwhgQtYLzNgIRoAZApiQzHDCUhiBekEAE7JeYMZGMALMEMCEZIYTlsII1AsCmJD1AjM2ghFghgAmJDOcsBRGoF4QwISsF5ixEYwAMwQwIZnhhKUwAvWCwP8DHPTd9RRQ52MAAAAASUVORK5CYII=[/img][/td][/tr][tr][td]Der Flächeninhalt eines Sektors ist näherungsweise[br] [math]\Delta A=\frac{1}{2}\cdot r\cdot r\cdot\Delta\varphi=\frac{1}{2}\cdot r^2\cdot\Delta\varphi[/math][br][br][size=85][br][/size][/td][td][/td][td]Der Flächeninhalt eines Sektors ist näherungsweise[br] [math]\Delta A = \frac{1}{2} \cdot \left| \vec{x} \times \overrightarrow{\Delta x} \right| = [br]\frac{1}{2} \cdot \left| \left( \begin{array}{} x \\ y \\ 0 \end{array} \right) \times \left( \begin{array}{} \dot{x} \\ \dot{y} \\ 0 \end{array} \right) \right| \cdot \Delta t [/math] [br] [math] = \frac{1}{2} \cdot \left( x \cdot \dot{y} - y \cdot \dot{x} \right) \cdot \Delta t[/math][/td][/tr][tr][td]Für die Summe aller Sektoren ergibt sich somit[br] [math]A = \frac{1}{2} \cdot \sum_{i=1}^n {r_i^2\Delta \varphi} [/math][/td][td][/td][td]Für die Summe aller Sektoren ergibt sich somit[br] [math]A=\frac{1}{2} \cdot \sum_{i=1}^{n} \left(x_i \cdot \dot{y_i} - y_i \cdot \dot{x_i} \right) \Delta t[/math][/td][/tr][tr][td]Im Grenzübergang für [math]n\longrightarrow\infty[/math] wird daraus[br] [math]\mathbf{A= \frac{1}{2} \cdot \int_{\varphi_1}^{\varphi_2} \left(r (\varphi) \right)^2 \mathbb{d} \varphi } [/math][/td][td] [/td][td]Im Grenzübergang für [math]n\longrightarrow\infty[/math] wird daraus[br] [math]\mathbf{A = \frac{1}{2} \cdot \int_{t_1}^{t_2} \left| x \cdot \dot{y} - y \cdot \dot{x} \right| dt}[/math][/td][/tr][/table]
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Information: Sektorenformel nach Leibniz