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

question 221

Multiple Choice

Evaluate the triple integral $\iiint _ { E } \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) d V$ in spherical coordinates, where E is the solid in the first octant bounded by the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4$ and the coordinate planes.

• A) \(\frac { 32 \pi } { 5 }\)
• B) \(\frac { 4 \pi } { 5 }\)
• C) \(\frac { \pi } { 2 }\)
• D) \(\frac { 2 \pi } { 3 }\)
• E) \(\frac { 16 \pi } { 5 }\)
• F)\(\pi\)
• G) \(\frac { 4 \pi } { 3 }\)
• H)2\(\pi\)

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