$$\int_C (xy+z^3)ds$$ $\vec{r}(t)= \langle \cos(t), \sin(t), t \rangle$ where $0 \leq t \leq \pi$ $$x=\cos(t)\\y=\sin(t)\\z=t$$
$\vec{r}'(t)=\langle -\sin(t), \cos(t), t\rangle $ $\| \vec{r}'(t) \| = \sqrt{\sin^2(t)+\cos^2(t)+1}= \sqrt{2}$ $$xy+z^3=\cos(t)\sin(t) +t^3$$ $$\sqrt{2} \int_0^\pi \cos(t)\sin(t) +t^3 dt$$ $$\sqrt{2} \int_0^\pi \cos(t)\sin(t) dt=0$$
$$ \sqrt{2} \int_0^\pi t^3dt= \frac{\pi^4 \sqrt{2} }{4} $$ The the answer is apparently $\frac{\pi^4 \sqrt{2} }{16}$. My question is where did I go wrong? Is this the right answer?