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## Homework Statement

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

## Homework Equations

[tex]\int \int F\cdot n dS=\int \int \int divF dv[/tex]

## The Attempt at a Solution

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?

thanks

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