Let $f(x,y,z)=x+yz$ and let $C$ be the line segment from $P=(0,0,0)$ to $(4,9,3).$

$($a$)$ Calculate $f(c(t))$ and $ds=||c^{\text{'}}(t)||dt$ for the parametrization $c(t)=(4t,9t,3t)$ for $0t1.$

$($b$)$ Evaluate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}f(x,y,z)ds.$

$($a$)f(c(t))=,ds=dt$

$($b$){\displaystyle \underset{C}{\overset{\phantom{}}{}}}f(x,y,z)ds=$