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Question Number 219423 by SdC355 last updated on 24/Apr/25

	Answered by SdC355 last updated on 24/Apr/25
	$S^→ (u,v)= { (((5/4)(1−(v/(2π)))cos(2v)(1+cos(u))+cos(2v))),(((5/4)(1−(v/(2π)))sin(2v)(1+cos(u))+sin(2v))),((((10v)/(2π))+(5/4)(1−(v/(2π)))sin(u))) :} 0≤u≤2π , −π≤v≤2π F^→ (x,y,z)=−xe_1 ^→ −ye_2 ^→ −ze_3 ^→ ∫∫_S F^→ ∙dS^→ =??$
	$\vec{S} (u, v) = {\begin{cases} \frac{5}{4} (1 - \frac{v}{2 π}) \cos (2 v) (1 + \cos (u)) + \cos (2 v) \\ \frac{5}{4} (1 - \frac{v}{2 π}) \sin (2 v) (1 + \cos (u)) + \sin (2 v) \\ \frac{10 v}{2 π} + \frac{5}{4} (1 - \frac{v}{2 π}) \sin (u) \end{cases}$ $0 \leq u \leq 2 π, - π \leq v \leq 2 π$ $\vec{F} (x, y, z) = - x {\vec{e}}_{1} - y {\vec{e}}_{2} - z {\vec{e}}_{3}$ $\int \int_{S} \vec{F} \cdot d \vec{S} = ? ?$
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