  Use the Divergence Theorem to compute the net outward flux of the field F=(2x, 3y, -z)  across the surface S where S is the boundary of the tetrahedron in the first octant formed by the plane x+y+z=3. Give the exact answer using pi as needed.

Question

Use the Divergence Theorem to compute the net outward flux of the field F=(2x, 3y, -z)  across the surface S where S is the boundary of the tetrahedron in the first octant formed by the plane x+y+z=3.

Give the exact answer using pi as needed.

Step 1

To calculate the net outward flux of the given vector field across the given surface

Step 2

The flux across the surface is a surface integral and the calculation is reduced to finding the volume integral thanks ot Divergence theorem

Step 3

The required flux is the integral of the divergence ...

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