Final answer:
The subject of the question is Mathematics, specifically vector calculus involving surface integrals, often applied in calculating electric flux through a surface in the presence of an electric field.
Step-by-step explanation:
The question you've asked involves integrating over the surface of a cube, which is a concept in mathematics. Specifically, it's related to the field of vector calculus and the computation of surface integrals. To calculate the surface integral of a cube in the first octant, one must consider each face of the cube separately due to the different orientations of the normal vectors on each face. The integration uses the bounds set by the edges of the cube and might involve the electric flux if the cube is exposed to an external electric field, like in the provided example.
For instance, the example provided indicates calculating electric flux through a plane, which is also a surface integral problem but specific to electric fields and flux. The computation in this context would involve taking the dot product of the electric field vector and the area vector, which becomes slightly more complex when the surface is not perpendicular to the field. According to the principles of electromagnetism, the flux would equal the dot product of the electric field and the area (E · A), adjusted for angle if necessary using a cosine term.
To calculate the surface integral one would apply the principles of vector calculus, using antiderivatives along two dimensions confined by the limits of the surface area of the cube. If the context involves electric flux, one might use Gauss's Law for a symmetrical shape to simplify the calculation, as with the sphere example provided.