Chapter 15.2, Problem 12ES

Let C be the curve represented by the equations $x=t,y=3t^2,z=6t^3(0\le t\le 1)$

In each part, evaluate the line integral along C.

$\begin{array}{l}\left(\text{a}\right){\displaystyle {\int }_C^{}xy{z}^2}d\text{s}\\ \left(\text{b}\right){\displaystyle {\int }_C^{}xy{z}^2}dx\\ \left(\text{c}\right){\displaystyle {\int }_C^{}xy{z}^2}dy\\ \left(\text{d}\right){\displaystyle {\int }_C^{}xy{z}^2}dz\end{array}$