Question ) Show that F is a Conservative Vector Field. (7b) Find the Potential Function f(x,y) for the Vector Field F. (7c) Evaluate W

(a) We are given – F=(14x+8y)i+(8x+18y)j, so M(x,y)=14x+8y and N(x,y)=8x+18y. Therefore My = Nx = 18, and the vector field is conservative. (b) To find a potential function, we integrate M and N: ∫(14x+8y)dx=7x^2+8xy+f(x) ∫(8x+18y)dy=8xy+9y^2+g(x) Combining the results, and eliminating the duplicate terms, we get f(x,y) = 7x^2+8xy+9y^2. (c) The endpoints of C are (0,−1) and (1,0). Therefore the Fundamental Theorem of line integrals gives ∫c F⋅dr=f(1,0)−f(0,−1) = −2. Learn about similar questions at : https://brainly.in/question/48817162 #SPJ4 Disclaimer : The complete question is given below. Question : (a) Show that the vector field F = (14x+8y)i + (8x+18y)j is conservative. (b) Find a potential function f such that F = ∇f (c) Use the potential to evaluate the line ∫c F⋅dr, where c is the part of the unit circle in the 4th quadrant. Reply

My=Nx=18, and the vector field is conservative.f(x,y)=7x^2+8xy+9y^2.∫c F⋅dr=f(1,0)−f(0,−1)=−2.Disclaimer: The complete question is given below.Question: