[Solution] Let n be the outer unit normal of the elliptical shell S: 4 x^2+9 y^2+36 z^2=36 for z ≥q 0. And let F=< y, x^2, sin (x^2+y^2) e^√3 z^7-5>
Question: Let \(\mathbf{n}\) be the outer unit normal of the elliptical shell \(S: 4 x^{2}+9 y^{2}+36 z^{2}=36\) for \(z \geq 0\). And let \(\mathbf{F}=\left\langle y, x^{2}, \sin \left(x^{2}+y^{2}\right) e^{\sqrt{3 z^{7}-5}}\right\rangle .\) Compute \(\iint_{S} \nabla \times \mathbf{F} d \mathbf{r}\)
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