利用无界函数积分的定义判别下列无界函数积分的敛散性.如果收敛,计算它的值.[tex=4.786x2.857]uBGT4Nt832AmQgX0Zp8/SgW+l4iCZxZHKYtoeQjh8IZZSBrIvo26jLHelcYSd3lG[/tex]

2022-05-28

利用无界函数积分的定义判别下列无界函数积分的敛散性.如果收敛,计算它的值.[tex=4.786x2.857]uBGT4Nt832AmQgX0Zp8/SgW+l4iCZxZHKYtoeQjh8IZZSBrIvo26jLHelcYSd3lG[/tex]

答案：

[tex=2.429x1.0]CN/1pboBqLxTG+spiDy+LQ==[/tex]是被积函数的奇点，故[tex=21.429x9.071]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[/tex]所以[tex=6.071x2.857]uBGT4Nt832AmQgX0Zp8/Sh81aQWBOa/NpAf0fjaGm2o0DWeWbnrxDS7u1o9OHWWE[/tex]收敛，且[tex=7.786x2.857]uBGT4Nt832AmQgX0Zp8/Sh81aQWBOa/NpAf0fjaGm2oxUVdS6z+LGcH3GuIQx46fXeZWMhVl6GJ8P4fJqWqmNg==[/tex]

举一反三

内容

0
利用无界函数积分的定义判别下列无界函数积分的敛散性.如果收敛,计算它的值.[tex=5.143x2.857]h0oFNrNfDLkjvUWNl512sEjFCe2zLTHnHaerdezTP7pdfsWTT/AZJIUlY3/Nsjx+JbynoQ6x26BnEuKdpgpi6A==[/tex]
1
利用无界函数积分的定义判别下列无界函数积分的敛散性.如果收敛,计算它的值.[tex=12.5x3.071]ED5ldIgITkqa/bhnUtQnkwg8Sh/bySse7//cyxYlFdLmoTtSgSl4R//rdJ21OBPClqOoBHfQH6j8Qu1diafhPw==[/tex]
2
判断广义积分的敛散性，如果收敛，计算广义积分的值[tex=4.786x2.857]D+OdHpWjBNPXoMUoCawgfgRygfpHj9Nfv8vEHTf1ab8XYMUM8XQZ2yUc69fyBkSq[/tex].
3
判别[tex=5.786x2.714]wJGaTThFo41W0bFf87CfUhqrppCtq3kP+exTBeGWe+Q=[/tex]的敛散性，如果收敛，计算反常积分的值.
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判别[tex=5.143x2.714]wJGaTThFo41W0bFf87CfUvIWGnlpdJBsTDEk5Xw7MsvWI0xvhz40WZHlTXsA6sng[/tex]的敛散性，如果收敛，计算反常积分的值.