Consider the parametric equation.

$x=t-2sin(t),y=1-2cos(2t),0t2$

$($a$)(3$ pts$)$ Set up $($but do not evaluate$)$ an integral that represents the arc length of the curve.

$($b$)(3$ pts$)$ Set up $($but do not evaluate$)$ an integral representing an area of the surface obtained by rotating the given curve about the x $-$axis.

$($c$)(3$ pts$)$ Set up $($but do not evaluate$)$ an integral that represents an area enclosed by the curve and the x $-$axis.