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A simple line integral

  1. Apr 6, 2017 #1
    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. jcsd
  3. Apr 6, 2017 #2

    Orodruin

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