Let F(x,y)=⟨4cos⁡(y),2sin⁡(y)⟩. Compute the flux ∮F⋅nds of F across the boundary of the rectangle 0≤x≤5,0≤y≤π2 using the vector form of Greens

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Margot Mill · Accepted Answer

Step 1 By using Green Theorem, ∮F.nds=∫x∫y(∂Q∂x−∂P∂y)dxdy =∫x=05∫y=0π2(∂(2sin⁡y)∂x−∂(2sin⁡y)∂y)dxdy =∫x=05∫y=0π2(0−2cos⁡y)dxdy =−10∫0π2cos⁡ydy =−10(sin⁡y)0π2 =−10(1−0) =−10 Step 2 CONCLUSION: The correct answer for the flux integral is -10.

Let F(x,y)=⟨4cos⁡(y),2sin⁡(y)⟩. Compute the flux ∮F⋅nds of F across the boundary of the rectangle 0≤x≤5,0≤y≤π2...

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