• 2022-06-29
    利用Green公式计算下列曲线积分:[tex=12.714x2.643]IjTYqeilRWF1DwJgwsQznocZlngiYQn12N4WNeP3Lpn6JHY31AalfcrA1CcRpBU+2fFsFd3BnUhVYKr7AcTswiXTH+ul4PxhzPt0CnIfwes=[/tex],其中[tex=0.714x1.0]Hl8mr56J4t0Ek5ZoqbFYYg==[/tex]是圆周[tex=5.143x1.571]OCj21ozeJQpB0WoBh2AdZF6fxdI5bV3paTQyBfJIzzU=[/tex]上由点[tex=2.286x1.357]sVCzP1QNUT517zJi7AAZqw==[/tex]到点[tex=2.286x1.357]jHMTqYcUIAXe+oo9ctTuxQ==[/tex]的一段弧.
  • 如图所示.[img=443x314]1797ecf4a1e017f.png[/img][tex=3.571x1.429]Bz3XjiAWN7ysq0xnvys3+BpN0ke+ZbrYqwBLGEMxHKg=[/tex],([tex=0.571x0.786]c5VsltFnl9nO0qB/vNKOWA==[/tex]从0到1),[tex=3.857x1.214]nzLALNuPyAM7fPcGspxna8Zd3lt8g681b7xthLU6aiw=[/tex]([tex=0.5x1.0]iwXm0SwS+lfupyC0IyH8yQ==[/tex]从0到1)[tex=32.714x3.429]q4/nv+4fHtZJ92cw48vPioK/jFcnhSb7++MAq4tsP8o+hn0Dw8EhYlNMSckyXoyDWOsfBfT0x4g8Pt4yQC3w7IB9CkB4AnaccFIFwWMZqEJjPZHny/qrZRkK+u18mWiTHDeBjz3Tb3BadBPuMlUUEjKTOacB8nZn9oDgXvC4VEMkMmgeq7DHzNpAoVa1qP9PVOZgpGoLGptwbbG5UyO73qbqpji1YCvz9yRHfaDpqur2r7SUyZzyHR0IiKw67vh2[/tex]原式[tex=33.857x2.857]KITfATi1YF7T/LwkKCV7e3aLx4Pdfm2cS8R0YDtrQlKYq5MMh1uzhPDrhVLiUP69zzbnRiHlDpljjHd3Y4YnyVhpGVWs3R5CwWXaZRqO4G2+XgptFFwZIy4D6R9BMnKcM/FGwsiC3JEOijfI0KhAj/Cq2BVCy5xZy8xzvvNjE+v9xvgpUFY2fbymvkpeJkK8iUIe8p6rGGPbQy1DGJu3pdDM6yGY0NmopXz4HbPgjwlj7a7wmETjyFpPjzIiQ36U[/tex][tex=14.143x2.929]la0vo8n7cYac13GO5EKQnL6Ib9hnYVcdw0FMXNlCNOtvRX6BewF+R8LXl+5cFsxXDBJNnP9dKi5dm5g1kHroaTvgLySMgPPJVKpsmnAiYpVQ7icYn/HzMnLNqE3Psxpb[/tex].
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    内容

    • 0

      计算积分 [tex=21.143x2.643]bh9kRMpSvIUsOuEq6YVyVGfzISFsLvvjSrD6vqjDhkQgsyO7tTsgIK5zI9VLvN3SrLDn/BKyMc3mgxDs0Jua+TKj6SD25xtWQxHrt3zFeGgre5n1Vc+dSbGrr0s7m5ME[/tex] 是沿[tex=2.286x1.429]HSZIS6c0/9yrldYs9Wy+gw==[/tex] 由 [tex=2.286x1.357]sVCzP1QNUT517zJi7AAZqw==[/tex] 到 [tex=2.286x1.357]OfHxxUhJ2mtIjsaijINmaA==[/tex] 点的弧段.

    • 1

      计算对坐标的曲线积分[tex=13.214x2.643]alcCPxjueKfpm1MgVjNCtYvAzXpPh0EYHtEumFiwpfYul/ZwN16SwUTsUZhhmnenUz8iSkN834WLott7PA8Cbj1tKNdMx3xetzrmAAzBhhY=[/tex],其中[tex=0.714x1.0]ravtxd2oof9d0U26ZFAIhw==[/tex]是抛物线[tex=2.786x1.429]UkfP67e9FepbHKgkEPFDeQ==[/tex]上从点[tex=3.0x1.357]bzPEcUvLA4PI9rTCrUAJtA==[/tex]到点[tex=2.286x1.357]IznYKk7kywvI5iLU+xoABA==[/tex]的一段弧。

    • 2

      计算对坐标的曲线积分:[tex=13.5x2.643]ppHuV5Fd6LU7ZKFVSTtZtBO2lN8kB5zVTpnte/r+rWN6iIbtewb5ZTSesh+Ekaxngiw+s9k5Cp5j+aGf3Dorsw==[/tex]其中[tex=0.714x1.0]ravtxd2oof9d0U26ZFAIhw==[/tex]是抛物线[tex=2.286x1.429]uhgOg8UGt89GFMkyJwpgXA==[/tex]上从点[tex=3.0x1.357]Ecil7H7MY9ciz7j7HTbQLA==[/tex]到点[tex=2.286x1.357]IznYKk7kywvI5iLU+xoABA==[/tex]的段弧

    • 3

      求 [tex=7.143x2.643]NmZ7LuJ9N4zbg1YyVa/RtiwSgsZ1mJH35vVdGhtrGzeAtq4+t0Bw4nzQygWt2+dJ[/tex]其中曲线 [tex=0.714x1.0]Hl8mr56J4t0Ek5ZoqbFYYg==[/tex] 是直线 [tex=1.857x1.0]iCWMESxH27wos2YIzODARQ==[/tex] 由原点到点 [tex=2.286x1.357]OfHxxUhJ2mtIjsaijINmaA==[/tex] 的一段.

    • 4

      计算下列曲线积分:[tex=3.5x2.643]WhaRO7dn0Z5IWuRUDXr7s55+0S0tI9BlLN8JEe520xw=[/tex],其中[tex=0.714x1.0]Hl8mr56J4t0Ek5ZoqbFYYg==[/tex]是[tex=2.786x1.429]ACKQQsei4y9ePqoXL8Psqg==[/tex]上从原点到点[tex=3.0x1.357]EOhL440P916InLemFLZ9Lw==[/tex]的一段弧.