 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-2/9/a/solution

Only the

x

component of the vector field is nonzero, so

F \cdot d r = (x^{2} + y^{2}) d x

. On the vertical segment,

d x = 0

throughout. Hence

\int_{C} F \cdot d r = 0 .

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