# Work of the field vector

• Apr 27th 2009, 07:47 AM
Apprentice123
Work of the field vector
What the work of the field vector $F(x,y) = (x^2,xy)$ to move a particle along the trajectory $r(t) = (2cost,2sint)$ for $0 \leq t \leq 2 \pi$

My solution:

$\int_0^{2 \pi} (-8cos^2tsent + 8cos^2tsent)dt$

$= 0$

Is correct ?
• Apr 27th 2009, 11:19 AM
Calculus26
Yes it is-- but since this a closed curve you could have checked yourself with Green's theorem as well
• Apr 27th 2009, 11:35 AM
Apprentice123
Quote:

Originally Posted by Calculus26
Yes it is-- but since this a closed curve you could have checked yourself with Green's theorem as well

Thank you