Answer :
For fluid moving in a vector field, the flux through the rectangle's perimeter is 750.52.
Flux = ∫ F. X ds
Flux = ∫∫ delta. F da (by divergence theorem)
delta. F = d/dx(x³+4) + d/dy(ycos(3x))
= 3x² + cos(3x)
So flux = ∫∫ 3x² + cos(3x) dy dx
= ∫ (3x² + cos(3x)) (y)⁶₀ dx
= 6 ∫ 3x² + cos(3x) dx
After evaluating,
= 6(125 + sin(15)/3)
= 750.52
Therefore, the flux through the boundary of the rectangle for fluid flowing along the vector field is 750.52
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