Evaluate the flux integral , where is the part of the surface inside the cylinder , oriented with normals pointing upward, and is the vector field ,
The answer is of the form submit the value of
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Ausgezeichnetes Problem!
∫ S G ⋅ d S = ∫ D ⟨ 0 , 1 6 − 2 x 2 − 2 y , 2 y − 2 y 2 ⟩ ⋅ ⟨ 2 x , 1 , 1 ⟩ d A = ∫ D ( 1 6 − 2 x 2 − 2 y 2 ) d A = ∫ 0 2 π ∫ 0 1 ( 1 6 − 2 r 2 ) r d r d θ = 1 5 π , where D is the disc x 2 + y 2 ≤ 1