Use the divergence theorem to find the outward flux of the vector field F(x, y,z)=2x2i+5y2j+3z2k across the boundary of the rectangular prism: 0≤x≤1,0≤y≤3,0≤z≤1.

In this exercise we have to calculate the flux by the divergent theorem:

By the divergence theorem, the flux of F across the boundary of a region, ∂R, is equal to the integral of div(F ) over the region itself, R. In this case, the flux would be:

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By the divergence theorem, the flux of F across the boundary of a region, ∂R, is equal to the integral of div(F ) over the region itself, R. In this case, the flux would be

if x = 1, then the answer is 3.5