Evaluate the Triple Integral $\iiint _ { E } \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) d V$

question 230

Multiple Choice

Evaluate the triple integral $\iiint _ { E } \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) d V$ , where $E = \left\{ ( x , y , z ) \mid x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \leq 1 \right\}$ .

• A) \(\frac { 2 \pi } { 3 }\)
• B) \(\frac { 2 \pi } { 5 }\)
• C) \(\frac { 4 \pi } { 3 }\)
• D) \(\frac { 4 \pi } { 5 }\)
• E)2\(\pi\)
• F) \(\frac { 6 \pi } { 5 }\)
• G) \(\frac { 8 \pi } { 3 }\)
• H) \(\frac { 8 \pi } { 5 }\)

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