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Consider the vector field F = <-y,-x>. Let C be the
semicircle y = v4-x^2 oriented counterclockwise from (2, 0) to (-2, 0).
Find the integral F * dr.
Solution
Vector field F is a conservative vector field with potential function -xy. So using
the fundamental theorem for line integrals we have -2 *0 - 2*0 = 0

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Consider the vector field F = -y,-x. Let C be the semicircle y =.pdf

  • 1. Consider the vector field F = <-y,-x>. Let C be the semicircle y = v4-x^2 oriented counterclockwise from (2, 0) to (-2, 0). Find the integral F * dr. Solution Vector field F is a conservative vector field with potential function -xy. So using the fundamental theorem for line integrals we have -2 *0 - 2*0 = 0