Evaluate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r).$

$13.$ vec$(F)(x,y)=($:$x^2{y}^3,x^3{y}^2$:$),C$:vec$(r)(t)=($:$t^3-2t,t^3+2t$:$),0t1.$

$15.$ vec$(F)(x,y,z)=($:$yz,xz,xy+2z$:$),C$ is the line segment from $(1,0,-2)$ to $(4,6,3).$

$17.$ vec$(F)(x,y,z)=($:$yz{e}^{xz},e^{xz},xy{e}^{xz}$:$),C$:vec$(r)(t)=($:$t^2+1,t^2-1,t^2-2t$:$),0t2.$

$19.$ vec$(F)(x,y)=($:$2x{e}^{-y},2y-x^2{e}^y$:$),C$ is any path from $(1,0)$ to $(2,1).$

$23.$ Find the work done by the force field vec$(F)(x,y)=($:$x^3,y^3$:$)$ in moving an object from $P=(1,0)$ to $Q=(2,2).$