Find the line integral of ∫ x+yz dx + 2x dy + xyz dz
C consists of line segments from (1,0,1) to (2,3,1) and from (2,3,1) to (2,5,2).
r=(1-t)<r0> + t<r1> 0<t<1
The Attempt at a Solution
I split up the two line segments into C1 and C2.
For C1 I got the parametric equation of x(t)=1+t, y(t)=3t, z(t)=1
I plugged this into the original equation also using dx=dt, dy=3dt, dz=0
This gave me the answer C1=13.
I then found the parametric equations of C2 to be x(t)=2, y(t)=3-2t, z(t)=1-t.
I plugged these into the equations again with their derivatives and got the answer to be -22/3.
I added C1 and C2 and got 17/3 as my answer.
The correct answer should be 97/3.