Answer
$18$
Work Step by Step
We know that the line equation can be expressed as:
$ r(t)=r_0+kt=(0,0,0)+t \lt 0,3,4 \gt=\lt 0, 3t, 4t \gt $
and $ x=0 \implies dx= 0 \\ y=3t \implies dy= 3 dt \\ z= 4t \implies dz= 4dt $
Substitute all the above values in the given integral as follows:
$ \int_{0,0,0}^{0, 3, 4} x^2 \ dx + yz \ dy +\dfrac{y^2}{z} \ dz \\=\int_0^1 0+36t^2 +18t^2 \\=[18t^2]_0^1 \\=18$
