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


  1. (a) We are given –
    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:
    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.
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    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.


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