In Section 17.1, we showed that if C is a simple closed
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In Section 17.1, we showed that if C is a simple closed curve, oriented counterclockwise, then the line integral is Area
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In Section 17.1, we showed that if C is a simple closed curve, oriented counterclockwise, then the line integral is Area enclosed by C = 1 2 C x dy ? y dx 1 Suppose that C is a path from P to Q that is not closed but has the property that every line through the origin intersects C in at most one point, as in Figure 7. Let R be the region enclosed by C and the two radial segments joining P and Q to the origin. Show that the line integral in Eq. (1) is equal to the area of R. Hint: Show that the line integral of F = ?y, x along the two radial segments is zero and apply Green
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