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

question 34

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.

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