Final answer:
To calculate the total flux of the vector field, integrate the dot product of the vector field and the area vector over the closed surface. Without specific details about the surface, it is difficult to provide a specific answer.
Step-by-step explanation:
To calculate the total flux of the vector field, we need to integrate the dot product of the vector field and the area vector over the closed surface. The vector field is given as f = xî + yĵ + zḱ, and the area vector is along the normal to the surface.
To find the total flux, we need to determine the limits of integration and the orientation of the surface. Without a specific figure or description of the surface, it is difficult to provide a specific answer. However, the general process is to parametrize the surface and calculate the dot product and the integration accordingly.
If you provide more details about the closed surface or describe it mathematically, I'll be able to assist you further.