# A simple line integral

Tags:
1. Apr 6, 2017

### Toby_phys

1. The problem statement, all variables and given/known data
Evaluate the following line integrals, showing your working. The path of integration in each case is anticlockwise around the four sides of the square OABC in the x−y plane whose edges are aligned with the coordinate axes. The length of each side of the square is a and one corner O is the origin.
(i) $\int dl$
(ii)$\int d\mathbf{l}$

2. Relevant equations

3. The attempt at a solution
i:
For each the sections OA and AB, the integral gets a value $a$. This is clear.

However, for the sections BC and CO, the change in x is in the negative x direction.

Basically I have 2 different answers $4a$ and $0$, which is correct? Thank you.

ii:

Same problem, I have 2 answers: $2a\mathbf{i} + 2a\mathbf{j}$ or $0\mathbf{i}+0\mathbf{j}$

2. Apr 6, 2017

### Orodruin

Staff Emeritus
I suggest you parametrise each segment and explicitly compute the integrals. Pay particular attention to the integration directions.