The discussion revolves around solving a line integral along a specified curve γ within the context of vector fields. Participants are exploring the complexities of substitutions and the potential path independence of the integral.
The discussion is ongoing, with participants providing guidance on examining the vector field's properties and suggesting checks for path independence. Multiple interpretations of the problem are being explored, particularly regarding the conservative nature of the field.
Participants mention the importance of start and end coordinates for the path and express uncertainty about the complexity of the problem. There are references to specific terms and derivatives within the vector field that may influence the approach taken.
I'm not sure. It looks overwhelmingly complicated to me.Orodruin said:
You might want to consider the start and end coordinates of the path (corresponding to ##t=0## and ##t= \pi##). You might want to consider whether or not the field is conservative.Graham87 said:
Compare the first terms of each expression. What do you see?Graham87 said:
Looks like some derivative or primitive function variation. But it's not in a series.Orodruin said:
There is really no "magic" too it. Just that ##3 x^2 y## is quite clearly the ##x##-derivative of ##x^3 y## ... of which ##x^3## is the ##y##-derivative, etc etcGraham87 said: