Let ${ \vec { F } } = x ( 1 + z ) \vec { i } + 7 y ( 1 + z ) \vec { j }$

question 7

Multiple Choice

Let ${ \vec { F } } = x ( 1 + z ) \vec { i } + 7 y ( 1 + z ) \vec { j }$ Show that the parametric surface S given by x = s cos t, y = s sin t, z = s, for 1 $\le$ s $\le$ 2, 0 $\le$ t $\le$ 2 $\pi$ , oriented downward can also be written as the surface $z = \sqrt { x ^ { 2 } + y ^ { 2 } } , 1 \leq z \leq 2$ . Which of the following iterated integrals calculates the flux of $\vec { F }$ across S? Select all that apply.

• A) \(\int _ { T } \frac { \left( x ^ { 2 } + 7 y ^ { 2 } \left( 1 + \sqrt { x ^ { 2 } + y ^ { 2 } } \right) \right. } { \sqrt { x ^ { 2 } + y ^ { 2 } } } d x d y\)
• B) \(\int _ { 0 } ^ { 2 \pi } \int _ { 1 } ^ { 2 } r ^ { 2 } ( 1 + r ) d r d \theta\)
• C) \(\int _ { 0 } ^ { 2 \pi } \int _ { 1 } ^ { 2 } r ^ { 2 } ( 1 + r ) n d \theta d r\)
• D) \(\int _ { 0 } ^ { 2 \pi } \int _ { 1 } ^ { 2 } r ^ { 2 } ( 1 + r ) \left( \cos ^ { 2 } \theta + b \sin ^ { 2 } \theta \right) d r d \theta\)
• E) \(- \int _ { T } \frac { \left( x ^ { 2 } + y ^ { 2 } \right) \left( 1 + \sqrt { x ^ { 2 } + y ^ { 2 } } \right) } { \sqrt { x ^ { 2 } + y ^ { 2 } } } d x d y\)

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