求下列曲面所围区域的体积：[tex=9.357x1.214]tC5WXgEjMTR/uC94hfLjIwEJsPqSCk5MjPtEWlUSBv8=[/tex]
解：体积V由两部分组成:[tex=19.5x5.357]Ck4j1YFlvVH5wCAykOEMi71D6IZfKQja0WSm+VzjKMIZRaug5Jx9azkockX6DFGrcHBKbCAK6hNcMzkD8m6wwrzLPr6qCZv1s5MUvGdxKcON6MeTrrwC+LrNz+nOXQczNeWVyWCg0vlJl4dH47fp+CRRo7SP06X5RF2sdzGeqEMgMWfDfGNvUhxBFxvPsNJqNm4HDdsqAvGcXbxO05/5A0IWJVGJlnr2ZziwAKPpTxKfUG0HF2xvZyCnOIILsXeimEtPvCun3Tmh7qgCImwoZw==[/tex]它们在Oxy平面上的投影域[tex=1.143x1.214]NqklA5xEfBOMiec3r6uq0g==[/tex]及[tex=1.143x1.214]UVaiuJTgiZc259jaFQqQ9w==[/tex]如图所示[tex=41.429x4.786]a0s3MH7cLIdmiBRR0YN06/fQSiqBU2fpexEShpYIOH5KaalTKSWKge023v8V68WPBy5DC/rJaG1HnTQgDVnwdLz/cxG/CR14YacsaJQiRVx/fFVIgT4zwOC5ux6zCHjquUBqGFWBWsNwxkIH6KKR1ypWQukyUdEXohOrD6+7zD+QszPKOSPB5WZMKNSHVqbku7REPZIN7VVMeEpozvZJYy/g51VhFo6RHpvPlHK8OZbcVfGBebiBORpBiV9tHZC1TV45u50SvIXjpQAp2KuSTpOXehfHvQw607dSzQd5p1AamMoxMfLJAxOwYRb+Me81yzKAvJYWbA6c7d8gq3sc7N608F4v98nPnRHUQLXYbuYSyC1wbA5oga9vpqky/vxxz20AjQH7lmpv+I0pI/ApgQ==[/tex]于是，所求的体积为[img=296x241]178d5526f5c85a3.png[/img]
举一反三
- 求下列曲面所围区域的体积：[tex=11.0x1.429]+e5DouuO5t0uQO1NFFXpeFk+6jda9byklz52olfv41+MhDtQkpDIBCq4QVROd7pq[/tex]
- 求下列曲面所围区域的体积：[tex=21.214x1.571]U37dn8znznFebviy+cQNpoyhcq5kPDS0bLRwOCFj4NKGCpJtKUaxmAdNpfC1hH9w4AMlJMWjrfFqhtytbkm42lYfvBWHN/pdr2Z9JLuii/g=[/tex]
- 变换成极坐标，求下列曲面所围成的区域的体积：[tex=12.071x1.571]5/zDgG6yUox2lb72MEhNyI5VAXFrADv2aSLlIvfsHAAV/oK5RY2LXeEU7nrwAEBsnts30HNNYd/xAkNnfoGHATKAWDlg7HqhI4Rh1jp5gXM=[/tex]
- 求下列曲面所围立体的体积：曲面[tex=5.214x1.429]eO+GzgNDaVFWKGy64CHSRfMASoJS+SMcA02cQOGdVs0=[/tex]，[tex=5.429x1.643]om0DX395gcXIzo/bROmkufWtqMtpIGjOXanzOoSlTUY=[/tex].
- 求下列曲面所围立体的体积：[tex=4.429x1.143]gGaSB0H7dT9N9/wJvrnk6A==[/tex]，[tex=4.643x1.429]MlIOqqYu5u1ffsbpFjlv5qsy4u6w8nSJ8jo5fVayDOs=[/tex]，[tex=6.571x1.571]R4SVfNVkSCVv5DUz4Y17qjFAGt5Q826lN7ia5jqx2qs=[/tex].
内容
- 0
求由曲面[tex=13.643x1.429]4CLkxHqXndfwc/JP+ksZltizC44D02kTRT7aQJrzSuySgd6X3cshBlmi/Hud25ux[/tex]所围立体的体积.
- 1
变换成极坐标，求下列曲面所围成的区域的体积：[tex=7.571x1.429]YYaH9U+AzBh0J5xtaeArtaPYlXWcIqr9xB7BvXofQhE=[/tex]
- 2
利用二重积分求下列立体[tex=0.786x1.0]b2qHHLl09vpLlE8vYMXmOw==[/tex]的体积：由曲面[tex=3.929x1.429]eXG42LBlVmCe9OBZMR2NwQ==[/tex]与[tex=5.0x1.643]L1mMyE+pmRrVhKGb1vNX3jcKQCSABiqdbvMy7sJs7Cg=[/tex]所围立体.
- 3
利用三重积分求下列曲面所围成的空间闭区域的体积:[tex=22.214x1.286]QwY3CbnOdl+ukx2Eamho1MTUIh+8ZqOAYbFle6UH9j3jvPXemjyIXv9ImJcmRg3+UjWhP8Kgzz2AacT9D76azRKtJjuKdXR8Az8roGfjqyA=[/tex]
- 4
求下列各族曲面所围成的立体体积 :[tex=15.071x1.429]rdWLgA4wIftDBhxsVgG6jDn16TJPOZqS+8J51G7jqb9s1sb8W3nrWsudY4dpjhkd[/tex]