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Calculus and Beyond Homework Help
How can I verify the Divergence Theorem for F=(2xz,y,−z^2)
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[QUOTE="kelvin56484984, post: 5717267, member: 585070"] [h2]Homework Statement [/h2] Verify the Divergence Theorem for F=(2xz,y,−z^2) and D is the wedge cut from the first octant by the plane z =y and the elliptical cylinder x^2+4y^2=16 [h2]Homework Equations[/h2] [tex]\int \int F\cdot n dS=\int \int \int divF dv[/tex] [h2]The Attempt at a Solution[/h2] For the RHS r(u,v)=(4cosu,2sinu,v) where u=[0,2pi] and v=[0,1] [tex]\overrightarrow{r}u \times \overrightarrow{r}v =(2cosu,4sinu,0) [/tex][/B] [tex]\left \| \overrightarrow{r}u \times \overrightarrow{r}v \right \|=\sqrt{4cos^{2}u+16sin^{2}v} [/tex] [tex]\int \int f(r(u,v))\cdot \left \| \overrightarrow{r}u \times \overrightarrow{r}v \right \| dudv [/tex] For the Div F . dv Div F=1 What is the limit for the triple integral? How can I do the triple integration to verify the divergence theorem? [FONT=Helvetica Neue][COLOR=rgb(51, 51, 51)] thanks [/COLOR][/FONT] [/QUOTE]
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How can I verify the Divergence Theorem for F=(2xz,y,−z^2)
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