Answer
$$-\pi $$
Work Step by Step
We know that the line equation can be defined as: $$ r(t)=r_0+kt=(0,0,0)+t \space \lt 3,3,1 \gt=\lt 3t, 3t, t \gt \\ x=3t \implies dx= 3 dt \\ y=3 \space t \implies dy=3 dt \\ z=2t \implies dz=2 \space dt $$
Substitute all the above values in the given integral as follows:
$$ \int_{0,0,0}^{3,3,1}18t \space dt-27 \space t^2 \space dt+\dfrac{-4}{1+t^2} dt=-\pi $$
