Q4 ### Use of Green's Theorem to Calculate Flux and Circulation#### Problem StatementUse Green's Theorem to find the counterclockwise circulation and outward flux for the field **F = (8x − 9y)i + (7y − 9x)j** and curve **C**: the square bounded by **x = 0**, **x = 8**, **y = 0**, **y = 8**.---#### Calculation Steps---**Question:** Calculate the outward flux:The outward flux is **[Input Box]**.*(Simplify your answer.)*---Green's Theorem relates a line integral around a simple closed curve **C** and a double integral over the plane region **D** bounded by **C**. It states:**∮C (P dx + Q dy) = ∬D ( (∂Q/∂x - ∂P/∂y) dA )**Given: - **P = 8x - 9y**- **Q = 7y - 9x**Use the partial derivatives:- **∂Q/∂x = ∂/∂x (7y - 9x) = -9**- **∂P/∂y = ∂/∂y (8x - 9y) = -9**The integrand becomes:- **∂Q/∂x - ∂P/∂y = -9 - (-9) = 0**Since the integrand is 0, the double integral of 0 over any region is 0, hence:**∬D 0 dA = 0**Thus, the outward flux around the given curve C is **0**.

Given that the field F=8x-9yi+7y-9xj and curve C: the square bounded by x=0,x=8,y=0,y=8. Use Green's…

Answered: Use Green's Theorem to find the…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.FOM: Focus On Modeling: Vectors Fields

Problem 11P

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Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F = (8x - 9y)i + (7y - 9x)j and curve C: the square bounded by x=0, x=8, y = 0, y = 8. The flux is (Simplify your answer.)