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.
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?