Solve the Problem $\mathrm { D }$ In Space Maximizes the Value of the Integral

Multiple Choice

Solve the problem.
-What domain $\mathrm { D }$ in space maximizes the value of the integral
$$\iiint \left( \frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 36 } + \frac { z ^ { 2 } } { 4 } - 1 \right) d V ?$$

A) $D =$ the boundary of the ellipsoid $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 36 } + \frac { z ^ { 2 } } { 4 } = 1$ .
B) $D =$ the boundary and interior of the ellipsoid $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 36 } + \frac { z ^ { 2 } } { 4 } = 1$ .
C) $\mathrm { D } = \mathcal { R } ^ { 3 }$
D) No such minimum domain exists.