$(20$ points$)$ Integrate $f(x,y,z)=xyz$ along the following path:

$(a)(5$ points$)c(t)=(e^{t}cost,e^{t}sint,3),0t2$

$(b)(5$ points$)c(t)=(cost,sint,t),0t2$

$(c)$ pointsc$(t)=\frac{3}{2}{t}^{2}i+2t^{2}j+tk,0t1$

$(d)$ pointsc$(t)=ti+\frac{1}{\sqrt[\phantom{2}]{2}}{t}^{2}j+\frac{1}{3}{t}^{3}k,0t1$