4. 积分域是以O(0, 0), A(2, 2), B(0, 2) 为顶点的三角形。交换积分次序I = ∫<0, 2>e^(-y^2)dy∫<0, y>dx = ∫<0, 2>ye^(-y^2)dy = -(1/2) ∫<0, 2>e^(-y^2)d(-y^2) = -(1/2) [e^(-y^2)]<0, 2> = (1/2)(1-1/e^2)L : x^2/4+y^2 = 1, 则 x^2 + 4y^2 = 4, 因 L 对称于 y 轴,2xy^2 是 x 的奇函数,则∮(x^2+2xy^2+4y^2)ds = ∮(4 + 2xy^2)ds = 4∮ds + 0 = 4a