Let $f(x,y,z)=x+yz$ and let $\mathcal{C}$ be the line segment from $P=(0,0,0)$ to $(2,6,2)$.

(a) Calculate $f(\mathbf{c}(t))$ and $\,ds=\Vert \mathbf{c}'(t)\Vert\,dt$ for the parametrization $\mathbf{c}(t)=(2 t,6 t,2 t)$ for $0\le t \le 1$.

(b) Evaluate $\int_{\mathcal{C}} f(x,y,z)\,ds$.

(a) $f(\mathbf{c}(t))=$ , $\,ds=$ $\,dt$

(b) $\int_{\mathcal{C}} f(x,y,z)\,ds=$