Answer
$$18$$
Work Step by Step
The line equation can be written as:
$ r(t)=r_0+kt=(0,0,0)+t \lt 0,3,4 \gt$
or, $r(t)=\lt 0, 3t, 4t \gt $
Now, $ x=0 $ and $dx= 0 $
and $y=3t $
or, $ dy= 3 dt$
and $ z= 4t $
or, $ dz= 4dt $
Now, we will substitute all the above values in the given integral.
$ \int_{0,0,0}^{0, 3, 4} x^2 \ dx + yz \ dy +\dfrac{y^2}{z} \ dz $
or, $=\int_0^1 0+36t^2 +18t^2 $
or, $=18 [t^2]_0^1 $
or, $=18$
