Question

设L为平面区域D:x^2+y^2+4x-2y

Answer 1

取L：x² + y² + 4x - 2y ≤ 0 ===> (x + 2)² + (y - 1)² ≤ 5

∮L (x² - y)dx + (- y² + 2x)dy

= ∫∫D [ ∂/∂x (- y² + 2x) - ∂/∂y (x² - y) ] dxdy

= ∫∫D [ (0 + 2) - (0 - 1) ] dxdy

= 3∫∫D dxdy

= 3(5π)

= 15π