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∏