[Solution Library] Calculate vecF • d r with the field F from problem #4, F(x, y, z)=[cy e^2 z , x e^2 z , 2 x y e^2 z+3 z^2] over the path γ parametrized
Question: Calculate \(\{\vec{F} \cdot d r\) with the field \(\vec{F}\) from problem #4,
\[F(x, y, z)=\left[\begin{array}{c}y e^{2 z} \\ x e^{2 z} \\ 2 x y e^{2 z}+3 z^{2}\end{array}\right]\]over the path \(\gamma\) parametrized by
\[\vec{r}(t)=\left[\begin{array}{c} \sin \left(\pi t^{2}\right) \cos ^{3}\left(\pi t^{2}\right) \\ \cos \left(\pi t^{2}\right) \sin ^{2}\left(\pi t^{2}\right) \\ \cos ^{3}\left(\pi t^{2}\right) \end{array}\right], \text { for } 0 \leq t \leq \sqrt{2}\]
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