Mathematics, 08.12.2019 16:31, Kigarya
What's the flux of the vector field f(x, y,z) = (e^-y) i - (y) j + (x sinz) k across σ with outward orientation where σ is the portion of the elliptic cylinder r(u, v) = (2cos v) i + (sin v) j + (u) k with 0 ≤ u ≤ 5, 0 ≤ v ≤ 2pi.
Answers: 2
![\mathbf r_u=\dfrac\partial{\partial u}[2\cos v\,\mathbf i+\sin v\,\mathbf j+u\,\mathbf k]=\mathbf k](/tpl/images/0409/0377/11a3d.png)
![\mathbf r_v=\dfrac\partial{\partial v}[2\cos v\,\mathbf i+\sin v\,\mathbf j+u\,\mathbf k]=-2\sin v\,\mathbf i+\cos v\,\mathbf j](/tpl/images/0409/0377/49cc1.png)
in the first integral, and the half-angle identity is used in the second. The first integral vanishes, leaving you with
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What's the flux of the vector field f(x, y,z) = (e^-y) i - (y) j + (x sinz) k across σ with outward...
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