Line Integral Along a Path: How to Compute and Use Vector Fields

[idir93]

1. Homework Statement

Vector field is F=-y\hat{x} + x\hat{y}

Compute the line integral along the path c(t)=( cos(t), sin(t) ) with 0≤t≤∏2. The attempt at a solution
i started computing f.dl but how much is dl ? I took it dx\hat{x} +dy\hat{y} I'm not sure if using Cartesian coordinates is right ?

 

[HallsofIvy]

I can's see why you would say " I'm not sure if using Cartesian coordinates is right" when everything is given in Cartesian coordinates. You are given that the line is defined by c(t)= (cos(t), sin(t)) so it should be clear that dc= (-sin(t), cos(t))dt and that is dl because it has unit length.

 

[idir93]

Found it ! it's 0.5∏