Use Green's Theorem to find the counterclockwisecirculation and outward flux for the field F and curve C.F=11x³y²i+x²yj4The outward flux is(Type an integer or a simplified fraction.)((0,0)y=x(3,3)сxy=x²-2xQK

Using Green's theorem for the vector field F = M i +N j, Circulation Outward flux

Answered: Use Green's Theorem to find the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(a) We consider the vector field F(x, y, 2) = (x², xy, 1) = x²ï+xyj+ 1k. (i) Calculate curl F = ▼ × F. (ii) Let the curve C be defined by the parameterization = {r(t) = (t, t², 1) , te (0,1)} . Calculate F - dr F - dr along this curve starting at the point A = (0,0, 1) and ending at B = (1, 1, 1).
Calculate the circulation of the field F around the closed curve C. Circulation means line integralF = x 3y 2 i + x 3y 2 j; curve C is the counterclockwise path around the rectangle with vertices at (0,0),(3,0).(3,2) and (0.2)
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Find the scalar potential for the conservative field: F(x, y, z) = 12xyi + (6x² − 6z²)j + (−12zy +9)k The scalar potential is $(x, y, z) = ¯ +C Use this fact to evaluate Jo curve joining the points P = (3,3,0) and Q = (0, -3, -4). [B C F. dr = 0 F. dr where C is a smooth
Compute the divergence and curl of the vector field cos? (x2 ) F = sin (²y=) 2. 10 yz4 – ryz , at the point (1, 1, c). a. Divergence = ab sin (a) f Ω b. Curl = sin (a) f Ω a 00
a) Find the values of a,b,c which make f(x,y,z) = sin (xay°z©) a potential function for the vector field F(x.y,z)= 4 x³y'z? cos (x*y z7) i+ 7x*y®z7 cos (x*y'z?) j + 7x*y?z® cos (x*y'z7) k a= b= c= b) Find the work of F along the curve r(t)=(2t, e t(t – 1), e tt – 1)) for 0sts1. Do not approximate your answer. For example, leave sin (e ) as that, not 0.41. Work = F•dr =

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Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and curve C. F=11x³y²i+1/x^yj ... (0,0) y=x (3,3) C y=x² - 2x