L is x ^ 2 + y ^ 2 = 4, calculate the value of ∮ L (x-yx ^ 2) DX + (XY ^ 2) dy I got 8 PI, I don't know, right Yes, it's the second kind of curve integral The guy who got PI, tell me how you got it
Substituting into polar coordinates, the upper and lower limits of integral are changed to 0 to 2 π x = 2cos θ, y = 2Sin θ∮ L (x-yx ^ 2) DX + (XY ^ 2) dy = ∫ - 2 (2cos θ - 8sin θ cos θ ^ 2) sin θ D θ + 2 (8cos θ sin θ ^ 2) cos θ D θ = ∫ - 4cos θ sin θ + 32sin θ ^ 2cos θ ^ 2) d θ = ∫ - 2sin2 + 8sin θ ^ 2) d θ =