Evaluate the integral ∫ V ∇ _ · r _ d V

Question

Evaluate the integral      ∫    V                        ∇        _    ·      r    _      d  V

massetereqe · Accepted Answer

r    _    =  (  x  ,  y  ,  z  ) and not   (  x  ,  y  ,      a    2    −      x    2    −      y    2    )  z  =      a    2    −      x    2    −      y    2   only on the paraboloid surface.  ∇  ⋅      r    _    =  3In polar coordinates,   0  ≤  z  ≤      a    2    −      ρ    2    ,  0  ≤  ρ  ≤  aSo the volume integral is,            ∫      0              2        π                    ∫      0                        a          2                            ∫      0                                    a            2                    −          z                      3         ρ         d    ρ         d    z         d    θ    =                  3        π                  a          4                    2

Evaluate the integral <msubsup> ∫ V <mrow class="MJX-TeXAtom-ORD">

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