Pregunta: ​​​​​​​ Calculate the following line integrals z C. F⃗ · ⃗d⃗r, where the vector field in two dimensions is given by F⃗ (x, y) = (2xy, x−2y). Furthermore, the curve C is described by the vector equation ⃗r(t) = (x(t), y(t)). More

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Calculate the following line integrals z C. F⃗ · ⃗d⃗r, where the vector field in two dimensions is given by F⃗ (x, y) = (2xy, x−2y). Furthermore, the curve C is described by the vector equation ⃗r(t) = (x(t), y(t)). More precisely, the parametrics are x(t) = sin t, y(t) = −2 cost, t ∈ [0, π]. (2) Calculate z C. x 2 y dx − y 2x day, where C is the circle of radius 1, x 2 + and 2 = 1. Check how they were the parametric equations of this curve. (3) Calculate the work done by the vector field F(x, y, z) = (e x , Hey , ez ) to move a particle along the curve described by the parametrics ⃗r (t) = (t, t2 , t3 ), where the parameter t ∈ [0, 2]. (4) Investigate how to graph a vector field analytically. Make a sketch of the vector field from the previous exercise, evaluating the at least 8 different points