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Need help on 2 problems

  1. May 18, 2008 #1
    Hey hows it going??

    I am having some trouble on this problem:

    Use Green's Theorem to evaluate the line integral
    ∫C F . dr
    where F =< y^3 + sin 2x, 2x(y^2) + cos y > and C is the unit circle x^2 + y^2 = 1 which is
    oriented counterclockwise.

    I started like so:

    ∫C Pdx + Qdy = ∫∫D Qx - Py dA

    Where P = y^3 + sin 2x
    Q = 2x(y^3) + cos y

    and
    Px = 3y^2
    Qx = 2y^2

    Now we have

    ∫∫D 2y^2 - 3y^2 dA
    = ∫(2π to 0)∫(1 to 0) 2y^2 - 3y^2

    Now I am confused on where to go or even if I did this correctly. Please help.

    The other problem I had trouble with goes as so:

    Find the maximum and minimum values of the function
    f(x, y) = x^2 + y^2 - 2x + y
    on the disc x^2 + y^2 ≤ 5.

    Solution:

    fx = 2x - 2 = 0 --> x=1
    fy = 2y + 1 = 0 --> y=1/2

    Pt(1, 1/2)

    Now we use Lagrange Multipler:

    (1) fx: 2x - 2 = λ2x
    (2) fy: 2y + 1 = λ2y
    (3) x^2 + y^2 = 5

    From here I know you have to solve for one of the equations then plug in.. I picked (2) to solve for y, but I am not sure how to solve it?? Or even if I approached this right.. Any help is appreciated.. Thank you.
     
  2. jcsd
  3. May 18, 2008 #2

    exk

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