Question

Let F(x,y)=⟨−8x,5y⟩ and let R be the rectangle with vertices (0,0),(8,0),(0,1), and (8,1). Compute the flux of F across the rectangle. Begin by parameterizing each side of rectangle (oriented counterclockwise), and then compute the flux integral over each side individually.

Answer 1

To compute the flux of the vector field F across the rectangle R, we need to parameterize each side of the rectangle and compute the flux integral over each side individually.

Step-by-step explanation:

To compute the flux of the vector field F across the rectangle R, we need to parameterize each side of the rectangle and compute the flux integral over each side individually. Let's define the sides of the rectangle as follows:

• Side 1: from (0,0) to (8,0)
• Side 2: from (8,0) to (8,1)
• Side 3: from (8,1) to (0,1)
• Side 4: from (0,1) to (0,0)

For each side, we can calculate the flux integral using the formula: Flux = ∫F⋅ds, where ds is the differential vector along the side.

By performing these calculations, we can find the flux of F across the rectangle R.