- #1

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## Homework Statement

##\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**

## 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.