
Line Integrals
I don't understand how to go about solving a problem of this form;
Integrate f(x,y,z)=x+ sqrt(y)  z^2 over the path C from (0,0,0) to (1,1,1) given by C=C1nC2uC3, where
C1: r(t)=tk , 0<t<1
C2: r(t)=tj + k , 0<t<1
C3: r(t)=ti + j + k , 0<t<1
Anyone have any suggestions??

If I understand correctly, the line integral for scalar functions is defined as
As
we may conclude that
Now, these derivatives on , , and are as follows:
In all cases, therefore, we end up with . Our task is now to find
The function is different for each :

Ok, this makes sense.
Is there a different approach when faced with a question like this;
Integrate f over the given curve: f(x,y) = (x+y^2)/(sqrt(1+x^2)) , C: y=(x^2)/2 from (1,1/2) to (0,0)
..Or is the same method applied.