设[tex=0.714x1.0]Hl8mr56J4t0Ek5ZoqbFYYg==[/tex]是由原点[tex=0.786x1.0]5SeCOJOzMwSNbX8MGx2Qsg==[/tex]沿抛物线[tex=2.786x1.429]8E7zaDCibVcB0xPC0P/7QQ==[/tex]到点[tex=2.857x1.357]EkAnep0M2EocAk1/8mlo7g==[/tex]，再由点[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]沿直线[tex=1.857x1.0]iCWMESxH27wos2YIzODARQ==[/tex]到原点的封闭曲线，则曲线积分[tex=9.143x2.643]9+30Z2I72wBgNOUoOg2ONaar15cJB1ieKlkhCvNlzrezh1XdQmKzBK8qS7uX9RbT+3YCdiIkn83ONT7yLU2Z8g==[/tex]

2022-06-06

设[tex=0.714x1.0]Hl8mr56J4t0Ek5ZoqbFYYg==[/tex]是由原点[tex=0.786x1.0]5SeCOJOzMwSNbX8MGx2Qsg==[/tex]沿抛物线[tex=2.786x1.429]8E7zaDCibVcB0xPC0P/7QQ==[/tex]到点[tex=2.857x1.357]EkAnep0M2EocAk1/8mlo7g==[/tex]，再由点[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]沿直线[tex=1.857x1.0]iCWMESxH27wos2YIzODARQ==[/tex]到原点的封闭曲线，则曲线积分[tex=9.143x2.643]9+30Z2I72wBgNOUoOg2ONaar15cJB1ieKlkhCvNlzrezh1XdQmKzBK8qS7uX9RbT+3YCdiIkn83ONT7yLU2Z8g==[/tex]

答案：

设由原点[tex=0.786x1.0]5SeCOJOzMwSNbX8MGx2Qsg==[/tex]沿抛物线[tex=2.786x1.429]8E7zaDCibVcB0xPC0P/7QQ==[/tex]到点[tex=2.857x1.357]k1fyl87ihgHd1j9V9uPr9A==[/tex]的一段曲线为[tex=1.071x1.214]ZOXh/l3GA7qPOudYV9VHDw==[/tex]，由点[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]到原点的一段直线为[tex=1.071x1.214]q7hrM1LOC7CBIDz/dGQ8+A==[/tex]，则[tex=19.071x13.071]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[/tex]

举一反三

内容

0
对 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]的不同值，分别求出循环群[tex=1.143x1.214]StMMJ6qThnpokZJIPGrdFyP3vrLnUdltYxmLxjw8za8=[/tex]的所有生成元和所有子群。(1) 7; (2) 8; (3)10 ;(4) 14 ; (5) 15 (6) 18 。
1
计算对弧长的曲线积分: [tex=2.929x3.571]zpUXNBsRswHMkmty62Ex2oNofzG9eH6oS7+Cdk16KT44FLYbTPtLC78LNeX5lYqu[/tex], 其中 [tex=0.714x1.0]Hl8mr56J4t0Ek5ZoqbFYYg==[/tex] 为由直线 [tex=1.857x1.0]iCWMESxH27wos2YIzODARQ==[/tex] 及抛物线 [tex=2.786x1.429]8E7zaDCibVcB0xPC0P/7QQ==[/tex] 所围成的区域的整个边界
2
计算下列曲线积分(其中[tex=2.429x1.071]Rgnw6H9bxYi8lkJDrClV2w==[/tex] ):[tex=3.071x2.643]qmfgt/3ojlEgXtEHbV2sitWM1AIUYaOOIAF65hpMDCQ=[/tex], 其中[tex=0.714x1.0]Hl8mr56J4t0Ek5ZoqbFYYg==[/tex]为由直线[tex=1.857x1.0]iCWMESxH27wos2YIzODARQ==[/tex]及抛物线[tex=2.786x1.429]8E7zaDCibVcB0xPC0P/7QQ==[/tex]所围成的区域的整个边界;
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
判断下列命题是否为真：（1）[tex=3.643x1.357]/5abqJjwKZ1qr+6hsVFF5EBvfq3ggOFNlHMClz0h9nk=[/tex]（2）[tex=2.929x1.357]rGJpyjIjJpbcoBTWxP0Jiw==[/tex]（3）[tex=4.5x1.357]2wycHMoqU83MyEp17iBils58bR7YLuCTI2G9NVAdlfY=[/tex]（4）[tex=5.214x1.357]CTz2gu+IIm1GgNmYMGaduCRtA41wnW4WqwRWwEhq6aA=[/tex]（5）[tex=4.857x1.357]1DcE2BMMOaZhTuxR/mjgsboXxfg5ET59Dp4I/jjEDuw=[/tex]（6）[tex=4.643x1.357]BSryrsQYOvTP2hTWRu6t4nAuJwlSs4L9jaq70EpB+Us=[/tex]（7）若[tex=6.0x1.357]y0IZLUnBO88nR8WBZYvd7QXv5S1OMINV5cQNzPyiyAc=[/tex]，则[tex=3.429x1.357]1brfPwTkVVIX4GfoMIUskA==[/tex]（8）若[tex=7.643x1.357]MhLfJXZnhbXiB0x3oNtFzThV4Y1mJxe1VYr7PkJE/T6hmTD3WWp+UxbNwvUQ6DHk[/tex]，则[tex=4.143x1.357]LZUA94ISo1po5HWsOVeBCjo0rMvj7uw3bGw5HiZenrI=[/tex]