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Line Integral (where the path is not single valued)

  1. Apr 5, 2009 #1
    I'm a bit confused as to how to solve this line integral:

    Evaluate I = The integral of (x+y)dx from A (0,1) to B (0,-1) along the semi-circle
    x^2 + y^2 = 1 for for x is equal to or greater than 0.

    So far have have got:

    if x^2 + y^2 = 1 then y= + SQRT of (1 - x^2)

    which I believe boils down to : 2 times the integral of SQRT (1 - x^2) from 0 to 1.

    I'm very confused how to finish this off and would appreciate any help.
  2. jcsd
  3. Apr 5, 2009 #2


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    Use polar coordinates! Ie: x = cos(theta), y = sin(theta), theta going from pi/2 to 3pi/2. (And include an overall negative sign due to the orientation of the curve)
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