Consider the cylindrical can of radius 1 with a

differentiable board in the counter-clockwise's direction. Calculate:

$\displaystyle \int\limits_C \vec{F} .d\vec{r} $:

$\displaystyle \vec{F} (x, y, z) = ( y(x-2), x^2y, z) $

OBS.: there is the figure of the cylinder and the curve, but it just says that the curve is closed and impossible to be parametrized.

A.: 3pi

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Attempt:

Parametrization: S --> (cosv, senv, u)

n = (-cosv, sinv, 0)

$\displaystyle \nabla\vec{F} = (0, 0, 6x^2 + 6y^2)$

$\displaystyle \nabla\vec{F}\vec{r}(u,v)\vec{n} = 0$

Where is the mistake?