Question: Calculate \(\int \nabla f \cdot d \vec{r}\) with where \(f(x, y, z) = x^{3} y^{3}-x^{2} z^{2}+y^{2} z^{3}\), over the path \(\gamma\) parametrized by \(\vec{r}(t)=\left[\begin{array}{c}3 \cos t-5 \sin t \\ 2 \cos ^{2} t-7 \sin ^{3} t \\ \sin ^{2} t \cos ^{2} t\end{array}\right]\) from \(t=0\) to \(t=\frac{3 \pi}{2}\).

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