I have read some discussion of the difference between scalar line integrals and line integrals, but I am still confused. For the problem: 1) Evaluate the scalar line integral $\int_{H}^{}$ $(x^2 + y^2 + z^2)$ds where H is the helix given by $\vec{c}^{\,}$(t) = $2cos(t)\vec{i}^{\,} + 2sin(t)\vec{j}^{\,} +2t\vec{k}^{\,}$, 0 $\leq$ t $\leq$2$\pi$. In the solution we do $\int_{0}^{2\pi}$ $4cos^2(t) + 4sin^2(t) +4t^2*\sqrt{4sin^2(t) + 4cos^2(t) + 4}$dt.
On the other hand for the problem: 2) Evaluate the line integral $\int_{C}^{}$ $(e^x\vec{i}^{\,} + xy\vec{j}^{\,})d\vec{s}^{\,}$ where C is parametrized by $\vec{r}^{\,}(t)=t\vec{i}^{\,}-t^2\vec{j}^{\,}, 0 \leq t \leq 1$. In the solution we get r'(t) = <1,-2t> and calculate $\int_{0}^{1} e^t(1) + t(-t^2)(-2t)dt$.
Why is that for the first one we use the square root of the derivative of $\vec{c}^{\,}$ in the square root and for the second we plug it in directly? Is it because the second problem is a line integral and the first is a scalar line integral? Any help is appreciated.