Final answer:
Evaluating a line integral involves parameterizing the curve, here the right half of a circle, and integrating a function along this parameterization, considering the differential arc length, which does not form a closed path.
Step-by-step explanation:
To evaluate the line integral along the right half of a circle, we typically parameterize the circle using a variable, often θ (theta), which represents the angle measured from the positive x-axis. Assuming we're dealing with a circle of radius r centered at the origin, the parameterization of the right half-circle (which spans from θ = 0 to θ = π) in Cartesian coordinates could be x = r cos(θ), y = r sin(θ).
Using this parameterization, the differential arc length, represented as dδ, will be r dθ, as the radius is constant. The line integral of a function along this curve is then computed by integrating from 0 to π, applying the given function to x and y obtained from the parameterization and multiplying by the differential arc length r dθ.
Note that the notation of a circle in the middle of the integral sign (∫∞) for line integrals indicates a closed path. However, since we're only evaluating the right half of the circle, this is not a closed path, and therefore the circle notation would not be used. The integration would capture the contributions along the half-circle, and it does not include the line segment that would close the half-circle to form a closed path.