1. ## Line integrals

1 - evaluate the line integral
(i used S as the integration sign)

S F.dr
c

where F=xi-zj+2yk

and c is the triangular path from(0,0,0)to (1,1,0) to (1,1,1) and back to (0,0,0)

2 - evaluate the line integral

S F.dr
c

F=(3x^2)i+2yzj+(y^2)k

where c is any path between the point (0,1,2) and (1,-1,7)

Any ideas on how to solve these, i'm at a complete loss

2. Originally Posted by macabre

and c is the triangular path from(0,0,0)to (1,1,0) to (1,1,1) and back to (0,0,0)
There much stuff here.

I think you are trying to parametrize the rectifiable curve.

You divide the line integral into 3 parts:
1)From (0,0,0) to (1,1,0)
2)From (1,1,0) to (1,1,1)
3)From (1,1,1) to (0,0,0)

For #1 use the curve,
<x,y,z>=<t,t,0> for 0<=t<= 1.
For #2 use the curve,
<x,y,z>=<1,1,t> for 0<=t<=1.
For #3 use the curve,
<x,y,z>=<t,t,t> for 0<=t<=1.

The evaluation I leave to thee.

3. ok i've finally figured out the first question...mostly..when you get the 3 answers for each line do you then sum the values or sum thr modulus of the values?

also for the second one what do you do with the the limit c? is it a case of finding a plane that passes through these two points?

4. Originally Posted by macabre
also for the second one what do you do with the the limit c? is it a case of finding a plane that passes through these two points?
Note it says any path. Thus it does not matter. I would chose a line (not plane) which passes through those points.

Their is another way (without actually find the curve parametrization). You need to find the scalar potention between these two points. Then use the fundamental theorem of line integrals.