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Example 4: Line Integral of a Circle

Find the line integral


where C is the circle x2 + y2 = 4, shown in Figure 13.2.13.


Figure 13.2.13

We may start at any point of C. Take (2,0) as the initial point. Then C has the parametric equations

x = 2 cos θ, y = 2 sin θ, 0 ≤ θ ≤ 2π.

As θ goes from 0 to 2π, (x, y) goes around C once counterclockwise as required.


Last Update: 2006-11-21