1. ## stocks integral

$
_{c}\oint F*dr=_{\sigma}\iint(curlF)nds
$

F(x,y,z)=(2z)i+(3x)j+(5y)k
$
_{\sigma}
$
is a part of a paraboloid $z=4-x^2-y^2$ where z>=0
on the x-y plane our paraboloid is 4=x^2+y^2
and the parametric view of it is:
x=2cost y=2sint z=0

so we get
$
_{c}\oint F*dr= (2z)dx+(3x)dy+(5y)dz
$

i cant understand the next step $

_{c}\oint F*dr= (2z)dx+(3x)dy+(5y)dz=\intop_{0}^{2\pi}[0+(6cost)(2cost)+0]dt
$

why??