1. The problem statement, all variables and given/known data
##\int_\mathscr{C} \vec{F}(\vec{r})\cdot d\vec{r}; \vec{F}(x,y,z) = <sin z, cos \sqrt{y}, x^3>## I am assuming ##\vec{r}## is the usual ##\vec{c}## used, so maybe this is where I am incorrect
3. The attempt at a solution
C goes from (1,0,0) to (0,0,3)
Parametrizing C
##\mathscr{C}: \vec{c}(t) = (1-t)<1,0,0> + t<0,0,3> = <1-t, 0 ,3t>; 0 \le t \le 1 ##
##\vec{c}\,\,'(t) = <-t, 0, 3>##
##\vec{F}(\vec{c}(t) = <\sin 3t, 1, (1-t)^3>##
##\displaystyle \int_{0}^{1} <\sin 3t, 1, (1-t)^3> \cdot <-t, 0, 3>dt##
##\displaystyle \int_{0}^{1} -t \sin 3t + 0 + 3(1-t)^3 dt##
I got this far and integrated it but got the wrong answer, I checked my integration already so I integrated this setup correctly but I screwed up on the setup somewhere.
