Green's theorem - area of a cycloid

[Feodalherren]

Homework Statement

Use Green’s Theorem to find the area of the region between the x – axis and one arch of the cycloid
parameterized by p(t) = < t-2sin(t),2-2cos(t)> for 0≤t≤2∏
p

Homework Equations

The Attempt at a Solution

My problem here is that I get different answers depending on if I use
F=<0,x> or F = <-y,0>

The 8∏ answer that I have to the right is the correct one. How do I know which force field to pick?

 

[Dick]

Homework Statement

Use Green’s Theorem to find the area of the region between the x – axis and one arch of the cycloid
parameterized by p(t) = < t-2sin(t),2-2cos(t)> for 0≤t≤2∏
p

Homework Equations

The Attempt at a Solution

My problem here is that I get different answers depending on if I use
F=<0,x> or F = <-y,0>

The 8∏ answer that I have to the right is the correct one. How do I know which force field to pick?

You can pick either one. The only problem is that you did the first integral wrong. The integral of t*sin(t) between 0 and 2pi isn't zero.