Respuesta :
As per the double integral, the flux of the vector is 2√11(6z + 1) + 176
What is double integral small definition?
In math, Double integrals are used to find the flux of a vector field through a given surface S and find the normal to the given surface and equations of the surface to find the limits of integration.
And it is calculate by the formula as Flux= ∫∫F⋅ndS
Here we have given that S be the part of the plane 2x + 1y + z = 2 which lies in the first octant, oriented upward.
And we need to find the the flux of the vector field F = 1i + 1j + 3k across the surface S.
As per the formula of flux of vector, it can be written as,
=>Flux = ∫∫(1i + 1j + 3k) . 2 dS
When we integrate this one the we get,
=> Flux = 2√11(6z + 1) + 176
To know more about Double integrals here.
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