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## Homework Statement

A closed curve C is described by the following equations in a Cartesian coordinate system:

where the parameter t runs monotonically from 0 to 2π, thus defining the direction of C. Calculate the area vector of the planar region enclosed by C, using the formula:

**2. The attempt at a solution**

I'm mostly having trouble defining what

Than I can evaluate it as:

and this would give a result that is only in the z direction which dimensionally makes sense