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Question: Multiple surface intersection.

Hi.

Lets say im given 2 surfaces like this:

S1: z=x^2+y^2 and S2: z=-2x

To find all the points on this surface i set z=z and obtain the equation, but lets say I was given an arbutary vectorfield and was required to find the outward flux I would need and parametric equation for the surface which is now a solid enclosed by 2 surfaces.

 

Of course I could apply the divergence theoreme and integrate the divergens over the entire volume using tripple integral. This I suppose this requires a bit more work compared to using the vector calculus package.

 

Would anyone give me an hint on ho to acheive this? Im also looking to plot the object crated by the bounderies of the divergenc theorem bounderies

Int(Int(Int(4*z, z = x^2+y^2 .. -2*x), y = -sqrt(-x^2-2*x) .. sqrt(-x^2-2*x)), x = -2 .. 0)

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