I'm trying to solve this line integral on Paul's notes: https://tutorial.math.lamar.edu/Solutions/CalcIII/LineIntegralsPtI/Prob2.aspx, but I don't know why my parametrization isn't working. For the curve I'm using the equation $(3cos(t), 3sin(t))$ from $π<t<2π$ and setting up the integral $3\int_{2\pi}^{\pi}54cos^2(t)sin(t)-12cos(t)dt$ since it asked for the surface to be clockwise, but I'm still getting the negative of the answer Paul's notes gives.
2026-04-02 17:42:52.1775151772
Why is my parametrization for this curve incorrect for this line integral?
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