$($f$){\displaystyle \underset{-C}{\overset{\phantom{}}{}}}f(x,y)ds=-{\displaystyle \underset{C}{\overset{\phantom{}}{}}}f(x,y)ds$

True

False

$($g$)$ There is a vector field $F$ such that curl $F=yjzk.$

True

False

$($h$)$ The area of the region bounded by the positively oriented, piecewise smooth, simple closed curve $C$ is $A=-o{\displaystyle \underset{C}{\overset{\phantom{}}{}}}ydx.$

True

False

$($i$)$ If $f$ has continuous partial derivatives of all orders on $R^3,$ then div$(curlgradf)=0.$

True

False

$($j$)$ The work done by a conservative force field in moving a particle around a closed path is zero.

True

False