Use the formula of vector calculus "Gauss's theorem or Divergence theorem" .. .it gives the relation between surface and volume integration. You will get right answer.
Attachment of photo is not happening in this application may be due to some error, otherwise I would send you the solution.

To find the value of the divergence theorem for the given field D = 2xy i + x^2 j, we need to evaluate the surface integral of the field over the rectangular parallelepiped and then calculate the volume integral of the divergence of the field over the same region. The divergence theorem states that the surface integral of a vector field over a closed surface is equal to the volume integral of the divergence of the vector field over the region enclosed by the surface.

1. Surface Integral:
To evaluate the surface integral, we need to calculate the flux of the vector field D across the six faces of the rectangular parallelepiped. The flux is given by the dot product of the vector field and the outward unit normal vector to each face.

The rectangular parallelepiped has six faces: top, bottom, front, back, left, and right. Let's calculate the flux across each face.

- Top face (z = 3):
The outward unit normal vector to the top face is k, i.e., (0, 0, 1). The dot product of D and the normal vector is:
D dot k = (2xy)(0) + (x^2)(0) = 0

- Bottom face (z = 0):
The outward unit normal vector to the bottom face is -k, i.e., (0, 0, -1). The dot product of D and the normal vector is:
D dot -k = (2xy)(0) + (x^2)(0) = 0

- Front face (y = 0):
The outward unit normal vector to the front face is -j, i.e., (0, -1, 0). The dot product of D and the normal vector is:
D dot -j = (2xy)(0) + (x^2)(-1) = -x^2

- Back face (y = 2):
The outward unit normal vector to the back face is j, i.e., (0, 1, 0). The dot product of D and the normal vector is:
D dot j = (2xy)(0) + (x^2)(1) = x^2

- Left face (x = 0):
The outward unit normal vector to the left face is -i, i.e., (-1, 0, 0). The dot product of D and the normal vector is:
D dot -i = (2xy)(-1) + (x^2)(0) = -2xy

- Right face (x = 1):
The outward unit normal vector to the right face is i, i.e., (1, 0, 0). The dot product of D and the normal vector is:
D dot i = (2xy)(1) + (x^2)(0) = 2xy

Now, we can calculate the surface integral by summing up the flux across each face:
Surface integral = (0 + 0 - x^2 + x^2 - 2xy + 2xy) = 0

2. Volume Integral:
To evaluate the volume integral, we need to calculate the divergence of the vector field D. The divergence of D is given by the sum of the partial derivatives of the components of D with respect to their respective variables.

div(D) = ∂(2xy)/∂x + ∂