用格林公式计算第二型曲线积分:∮(x²-y)dx+(y²+3x)dy
范围L::∣x∣+∣y∣=1
人气：468 ℃ 时间：2019-12-22 21:15:37
解答
令P = x² - y
∂P/∂y = - 1
令Q = y² + 3x
∂Q/∂x = 3
则∮_(L) (x² - y) dx + (y² + 3x) dy
= ∫∫_(D) (3 - (- 1)) dxdy
= 4∫∫_(D) dxdy
= 4 * 4 * (1/2)(1)(1)
= 8
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