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## Homework Statement

Use the divergence theorem to evaluate

[itex]\int\int_{\sigma}F . n ds[/itex]

Where n is the outer unit normal to [itex]\sigma[/itex]

we have

[itex]F(x,y,z)=2x i + 2y j +2z k [/itex] and [itex]\sigma[/itex] is the sphere [itex]x^2 + y^2 +z^2=9[/itex]

## Homework Equations

[itex]\int\int_{s}F . dA = \int\int\int_{R}divF dV[/itex]

## The Attempt at a Solution

I've worked out [itex]divF[/itex] to be 6.

so I multyiply that by the Volume of a sphere [itex]6\times\frac{4}{3}\pi r^3 = 216\pi[/itex]

To calulate this using spherical co-ordinates.

I would need to calculate a triple integral

I know theres

[itex]\int\int\int p^2 sin(\theta) dp d\theta d\phi[/itex]

I know that p = 3 but what would the values of [itex]\theta [/itex] and [itex]\phi [/itex] be

I guess the limits would be [itex]0<p<3[/itex][itex] 0<\phi<2pi[/itex] and [itex]0<\theta<\phi[/itex]

Any help greatly appreciated

## Homework Statement

## Homework Equations

## The Attempt at a Solution

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