Evaluating Line Integral: Curl of F and its Relation

[Frenchy]

1. Evaluate the line integral∫F . dr with F = 3(-y,x,0) from (a,0,0) to (a,0,2πb) along a straight line.

2. Do the same along a circular helix between the two points, parameterised as r = (a cosλ, a sinλ, bλ)

3. Compute the curl of F. How does this relate to the two integral calculations above?

I know Curl = \nabla x F

My notes on this don't seem to be that great, and I'm just completely lost, tbh.

Any help?

 

[BrendanH]

It should seem obvious that, since there is no force applied in the z in the first one, no work is done. From experience, I know that it is again zero in part 2. What do you get for the curl? Solving for it should show you tell you something important.

 

[Vid]

http://tutorial.math.lamar.edu/Classes/CalcIII/LineIntegralsIntro.aspx

Read these notes, make an attempt, and then we'll help you with any questions you have.