二空间立体Q的体积V=∫lh 5JZ1-32dxdy=Jfi(x, y)-f2(x, y)dxc y ex3计算由曲面z=x2+2y2及z=6-2x2-y2所围成 的立体体积 Solution.立体在xoy面上的投影区域为 D:x2+y2≤2 6-2x2-y2)-(x2+2y2)xhy D 16-3(x2+y2)xay (6-3rrdrd6 D D 2丌 6n(6-3r2)rt=6兀 K心二.空间立体的体积 =  − =  − Dxy Dxy V z z dxdy f (x, y) f (x, y)dxdy 1 2 1 2   V = dv . 3. 2 6 2 2 2 2 2 的立体体积 ex 计算由曲面z = x + y 及z = − x − y 所围成 Solution. o x y z 立体在xoy面上的投影区域为: : 2, 2 2 D x + y  =  − − − + D V [(6 2x y ) (x 2y )]dxdy 2 2 2 2 =  − + D [6 3(x y )]dxdy 2 2 =  − D (6 3r )rdrd 2 =   − 2 0 2 2 0 d (6 3r )rdr   = 6