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Thread: Line Intergral

  1. #1
    Junior Member
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    Line Intergral

    Compute the value of the line integral.

    integral(y dx + z dy + x dz),

    where the path to integrate on is the curve of intersection of the two surfaces x + y = 2 and x^2 + y^2 + z^2 = 2(x + y). The curve is to be traversed once n a direction that appears clockwise when viewed from the origin.

    My main problem is understanding the curve (path) that we need to integrate on. Any help?
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  2. #2
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    You need to parametrize the curve. First, since x+y = 2, y = 2 - x, So, letting x = t, we have y = 2 - t, and

    t^2 + (2 - t)^2 + z^2 = 4

    Solve this last equation for z to get z in terms of t.

    I hope this gets you started.
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