Calculate

${\int}_{\mathrm{\partial}F}2xy\phantom{\rule{thinmathspace}{0ex}}dx+{x}^{2}\phantom{\rule{thinmathspace}{0ex}}dy+(1+x-z)\phantom{\rule{thinmathspace}{0ex}}dz$

for the intersection of $z={x}^{2}+{y}^{2}$ and $2x+2y+z=7$. Go clockwise with respect to the origin.

${\int}_{\mathrm{\partial}F}2xy\phantom{\rule{thinmathspace}{0ex}}dx+{x}^{2}\phantom{\rule{thinmathspace}{0ex}}dy+(1+x-z)\phantom{\rule{thinmathspace}{0ex}}dz$

for the intersection of $z={x}^{2}+{y}^{2}$ and $2x+2y+z=7$. Go clockwise with respect to the origin.