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Use a graph of the vector field $ \textbf{F} $ and the curve $ C $ to guess whether the line integral of $ \textbf{F} $ over $ C $ is positive, negative, or zero. Then evaluate the line integral.

$ \textbf{F}(x, y) = \dfrac{x}{\sqrt{x^2 + y^2}} \, \textbf{i} + \dfrac{y}{\sqrt{x^2 + y^2}} \, \textbf{j} $,

$ C $ is the parabola $ y = 1 + x^2 $ from $ (-1, 2) $ to $ (1, 2) $

Line Integral is zero

Vector Calculus

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