Parametrization of the first segment:
x=t+1, y=4t, z=1 wherein t is on the segment [0,1].
Second segment:
x=2, y=2t+4, z=2t+1 and again t is in [0,1].
Compute the derivatives like this:
First segment: dx=1dt, dy=4dt, dz=0
Second segment:dx=0, dy=2dt, dz=2dt.
Using the above variables, the given integral becomes like this:
[tex]\int_0^1(((t+1)+4t)dt+2(t+1)4dt)+(4\times2dt+2(2t+4)(2t+1)2dt)[/tex]
The above integral is classical, and simple computation we obtain:
[tex] \frac{389}{6} [/tex]
