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.