1. 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?

2. 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.