Answer
$26 \sqrt {13}$
Work Step by Step
Here, we have
$ ds=\sqrt {(\dfrac{dx}{dt})^2+(\dfrac{dy}{dt})^2+(\dfrac{dz}{dt})^2} dt$
and $ds= \dfrac{\sqrt {13}}{3} dx$
This implies that
$\int_C f(x,y) ds= (\dfrac{\sqrt {13}}{3}) \int_{0}^{6} 8+\dfrac{5x}{3} dx$
Thus, we have
$ (\dfrac{\sqrt {13}}{3})[8x+\dfrac{5x^2}{6}]_0^{6}=26 \sqrt {13}$
