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问答题

设曲线积分∮L2[xφ(y)+ψ(y)]dx+[x2ψ(y)+2xy2-2xφ(y)]dy=0,其中L为任意一条平面曲线。求:  (1)可微函数φ(y)、ψ(y)。已知φ(0)=-2,ψ(0)=1。  (2)求沿L从原点(0,0)到点M(π,π/2)的曲线积分。

发布日期:2021-04-03

设曲线积分∮L2[xφ(y)+ψ(y)]dx+[x2ψ(y)+2xy2-2xφ(y)]dy=0,其中...

试题解析

曲线积分

在数学中,曲线积分是积分的一种。积分函数的取值沿的不是区间,而是特定的曲线,称为积分路径。曲线积分有很多种类,当积分路径为闭合曲线时,称为环路积分或围道积分。曲线积分可分为:第一类曲线积分和第二类曲线积分。

中文名
曲线积分
基本简介
∫ρ(x,y)ds叫对弧长的曲线积分
类别
第一、二类曲线积分
外文名
Line Integral
定义
弧长曲线积分也叫第一类曲线积分
应用
重力场

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