Let $\mathbf { F } ( x , y , z ) = x \mathbf { k }$

question 64

Multiple Choice

Let $\mathbf { F } ( x , y , z ) = x \mathbf { k }$ . Evaluate the surface integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ , where S is that part of the plane $z = x$ that lies above the square with vertices $( 0,0 ) , ( 1,0 ) , ( 0,1 )$ , and $( 1,1 )$ and has upward orientation.

• A) \(1\)
• B)\(\sqrt { 2 }\)
• C)\(\sqrt { 3 }\)
• D) \(2\)
• E)\(\frac { \sqrt { 2 } } { 2 }\)
• F) \(\frac { \sqrt { 3 } } { 2 }\)
• G) \(\frac { 1 } { 2 }\)
• H) \(\frac { 1 } { 4 }\)

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