Let And Let S Be the Boundary Surface of the Solid

question 231

Multiple Choice

Let $\mathbf { F } ( x , y , z ) = \sin \left( y ^ { 2 } + z ^ { 2 } \right) \mathbf { i } + \cos \left( x ^ { 2 } + z ^ { 2 } \right) \mathbf { j } + e ^ { z ^ { 2 } + y ^ { 2 } } \mathbf { k }$ and let S be the boundary surface of the solid $E = \left\{ ( x , y , z ) \mid x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \leq 1 \right\}$ . Evaluate the surface integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ .

• A) \(0\)
• B) \(\frac { \pi } { 4 }\)
• C) \(\frac { \pi } { 3 }\)
• D) \(\frac { \pi } { 2 }\)
• E) \(\frac { 2 \pi } { 3 }\)
• F) \(\frac { 3 \pi } { 4 }\)
• G) \(\pi\)
• H) \(\frac { 3 \pi } { 2 }\)

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