- #1
thercias
- 62
- 0
Homework Statement
Consider a vector A = (x^2 - y^2)(i) + xyz(j) - (x + y + z)k and a cube bounded by the planes x = 0, x = 1, y = 0, y = 1, z = 0 and z = 1
Determine the volume integral ∫∇.A dV where V is the volume of the cube
Determine the surface integral ∫A.n dS where s is the surface of the cube
Homework Equations
The Attempt at a Solution
∇.A = 2x + xz -1
Volume integral = ∫∫∫(all from 0 to 1) (2x + xz -1)dxdydz
=1/4 (after simplifying)
Surface integral = (all from 0 to 1) ∫∫(x^2-y^2)dydz + ∫∫(x+y+z)dxdy + ∫∫(xyz)dxdz
this simplifies to a more complicated term
I know that both of these methods must lead to the same answer, so I know that I must be doing something wrong with assigning the integrals to evaluate. Can someone show me how to properly set up the volume and surface integrals? This is what I'm confused about the most.