The trumpet surface, S, is given parametrically by $$\vec { r } ( s , t ) = s \vec { 2 } \cos t \vec { i } + s \vec { j } + s ^ { 2 } \sin t k , 0 £ s £ 5,0 £ t £ 2 \pi$$ If S has outward pointing normal, use an appropriate line integral to calculate $\hat { Q } { \operatorname { curl } } ( z \vec { i } + \cos ( x + z ) \vec { j } - x \vec { k } ) \times \vec { d A }$

Question

The trumpet surface, S, is given parametrically by $$\vec { r } ( s , t ) = s \vec { 2 } \cos t \vec { i } + s \vec { j } + s ^ { 2 } \sin t k , 0 £ s £ 5,0 £ t £ 2 \pi$$  If S has outward pointing normal, use an appropriate line integral to calculate $\hat { Q }  { \operatorname { curl } } ( z \vec { i } + \cos ( x + z ) \vec { j } - x \vec { k } ) \times \vec { d A }$

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The Answer of The trumpet surface, S, is given parametrically by $$\vec { r } ( s , t ) = s \vec { 2 } \cos t \vec { i } + s \vec { j } + s ^ { 2 } \sin t k , 0 £ s £ 5,0 £ t £ 2 \pi$$  If S has outward pointing normal, use an appropriate line integral to calculate $\hat { Q }  { \operatorname { curl } } ( z \vec { i } + \cos ( x + z ) \vec { j } - x \vec { k } ) \times \vec { d A }$

The Trumpet Surface, S, Is Given Parametrically By r⃗(s,t)=s2⃗cos⁡ti⃗+sj⃗+s2sin⁡tk,0£s£5,0£t£2π\vec { r } ( s , t ) = s \vec { 2 } \cos t \vec { i } + s \vec { j } + s ^ { 2 } \sin t k , 0 £ s £ 5,0 £ t £ 2 \pir(s,t)=s2costi+sj​+s2sintk,0£s£5,0£t£2π

The Trumpet Surface, S, Is Given Parametrically By $\vec { r } ( s , t ) = s \vec { 2 } \cos t \vec { i } + s \vec { j } + s ^ { 2 } \sin t k , 0 £ s £ 5,0 £ t £ 2 \pi$