Correcting Errors in Conservative Line Integral Calculation

[fonseh]

Homework Statement

I am having question with part c , for both c1 and c2 , here's my working for c1 , i didnt get the ans though . My ans is -5 , but the given ans for c1 and c2 is 27 , is the ans wrong ? Or which part i did wrongly ?

Homework Equations

The Attempt at a Solution

 

[Charles Link]

$z=0$ in the $\hat{j}$ term, and the $\hat{k}$ term in $d \vec{r}/dt$ equals zero, so that both the $\hat{j}$ and $\hat{k}$ terms are equal to zero. You left off the $t$ term in the $\hat{i}$ integral term. With these corrections, I think you will get the correct answer.