求由球面[tex=7.929x1.286]QwY3CbnOdl+ukx2Eamho1DXar6vx95H1kUSQO6EQd9M=[/tex]与柱面[tex=5.929x1.286]9bZQpSYifgquBYPcQEiZpyeLMnDjRCROeFJYCnAIQyk=[/tex]所围成立体的体积[tex=0.857x1.286]ZpwhzmyivskaH5M1X7ozaQ==[/tex]（指含在柱体内的部分），如图所示。[img=271x256]1783f308af8ba1a.png[/img]

2022-06-19

求由球面[tex=7.929x1.286]QwY3CbnOdl+ukx2Eamho1DXar6vx95H1kUSQO6EQd9M=[/tex]与柱面[tex=5.929x1.286]9bZQpSYifgquBYPcQEiZpyeLMnDjRCROeFJYCnAIQyk=[/tex]所围成立体的体积[tex=0.857x1.286]ZpwhzmyivskaH5M1X7ozaQ==[/tex]（指含在柱体内的部分），如图所示。[img=271x256]1783f308af8ba1a.png[/img]

答案：

解：由于球面与圆柱面所围成的立体关于[tex=1.571x1.286]woV9XOBscX2hvkxmcnGdWw==[/tex]坐标面、[tex=1.5x1.286]OeIxCzxOjrNwqeWrgfpLuA==[/tex]坐标面对称，故所求体积为[tex=11.071x3.357]rffmoP3M9wznatIQ0D6VMW37CDTqNyAlWu1kpHM0oZ1YFmSAIQafHIDPJReIkR0rP4HCAPpyOhBJffziiYd8OJP0JbfvbfTvb4yptFxAsCE=[/tex]其中积分区域[tex=0.857x1.286]s+r8LBAs3scxfl88DGExcg==[/tex]为第一象限的半圆[tex=5.0x1.429]de/325lPCNr4Nj88UnWu6o8l67iVedVMYtzgWbC+BZY=[/tex]与[tex=0.571x1.286]Hz6y44ELFVLLNrLVhO3CQA==[/tex]轴围成（如图）；曲顶为[tex=1.571x1.286]woV9XOBscX2hvkxmcnGdWw==[/tex]坐标面上方的球面[tex=7.143x1.643]W7H1GFIJVrue9e04eBqJwXvRbBi6rDc/Kqy212TJhOYVmhYoofGZ4Zn/6r/7z9UU[/tex]。[img=237x257]1783f3604a1b8f2.png[/img]将圆的方程[tex=5.0x1.429]de/325lPCNr4Nj88UnWu6o8l67iVedVMYtzgWbC+BZY=[/tex]化为极坐标形式[tex=4.357x1.214]5S8BzGYLMDpyfElq4SOeoRV1+JEUJdfFoN1iZMU7yx0=[/tex]在极坐标系下[tex=0.857x1.286]s+r8LBAs3scxfl88DGExcg==[/tex]为：[tex=8.643x3.929]GE56u9QCDTqcLxZ66HADylbuKSgDZ8QsXg8CRxPEVkPap6uaj/+zaGjD/K0L33GTaKo3Mly5hl8TlbUNuYPL4zEB2V3kdcBrsof96VpXNP2e3Iqpio6/AXIE1tllDbzc9xK0qjo1tnWlUnrzPGbiDyKqn01sr3G3wHk354LlGza/4S/NAKgsl1TOkFzzB352[/tex]于是[tex=21.286x3.357]rffmoP3M9wznatIQ0D6VMW37CDTqNyAlWu1kpHM0oZ1YFmSAIQafHIDPJReIkR0rP4HCAPpyOhBJffziiYd8OJ/IlFwHlVJTyLDSZaBenOXIY1JMAW+91tAL4dwQ9BOgf2nBxYoLnEDyu3nSgLv4j46ve1n1hy0APNRzhbnuvxxwXc3Fbzw6chBVHwDGts0DUI1jpKkv516qC4WQK4WyeA==[/tex][tex=14.643x2.857]gvJS5G8i30Qw3a3mnJYnOLo2LrEtc+EXh8ceVWPtVvn9JDjcWKDVTQMRKhtBpOnj+HzXF2491Ro/h3tgIADQJ/uH8EvB3UeCccuNb9ILWmXw2B9QbQ3sovkxxTADoiGeqkPTszDEs1/JR+uq5Xn40rBYT9pSBT5kEvHZRgQHJG8=[/tex][tex=13.286x3.0]NTRHXRsX6+E5Ouzy+BsGzzt2bYjsn6MmHT0/sCfWQIrVfscsYj1oN0uNqiesVXv/pIoWtCizW/E+zSzhcmfBv7k1x2eEGXB+DaoDPgl1yjVah3R7tLUYPaIyaJHBn31DMwG4MIU8xIRJl62U4rTtcyQzWEDeCNpGZTYUdn/3ufdaJ/CWdUhgdo2Ibz2rLZWJ[/tex][tex=18.857x2.929]A/oDx1h5oWQK1vuXPRoUWtOum0FoyBcjoa4L56myENplJv43xMMN8PbMpQUQAlkR7k8nrmTUgMYS73fwxpu5qOceOTZMN7S8ZJvVUNeNF2c4S+qpdo8ON8o5F/gmxzScTiDmgKTD5+Qz6hWqefbl3At3cMP9vitvjz3mXArXf3s/MXIdRQx8ixyl8xOi6oZSahqrlxJDqIfwCbdGIR7x8g==[/tex]。

举一反三

内容

0
设随机变量X的密度函数为[img=572x74]1791bc8f97085d2.jpg[/img]试求：（1）常数A；（2）[tex=6.714x1.357]AyFmD19eLybEpNdIrC346g==[/tex]
1
求下列函数的导函数：(1) [tex=5.0x2.357]X/CieCDGJ7iPQ3YFWuscHxHrcIE/dPFa9tFyiJXze8A=[/tex](2)[tex=6.643x1.714]Oj74y/L+OxY81QME5JWMcl+7PZ2FGQswwvjgVhjq1Dmb6dBU0oAjZBW7eFBVjqo6[/tex]
2
求柱面 [tex=3.929x1.429]/zgqabtImeIaKGhfpDlfIA==[/tex] 与三张平面 x =0, y = x , z =0 所围的在第一卦限的立体的体积。
3
利用二重积分求下列平面区域的面积：D由曲线[tex=5.357x1.357]2NfaP9ROOJ6D5nymLnK1v+3fCO7nkzkXSWZaetG9bmQ=[/tex]及x=1围成
4
某人对商品x的需求函数是[tex=5.214x1.214]0m6eBd5eyK0NjuxeKfwtIw==[/tex]，[tex=4.214x1.214]I717YsPbj8Rnym1v2XQ+sFNkUl7mqUsGwbjwjXmy2xc=[/tex]，这里[tex=0.571x1.0]Za328cIB4SeR7rrzY+MM5Q==[/tex]是[tex=0.571x0.786]ZSLOI4fiO1oAbVC5M8IVkA==[/tex]的价格。如果商品x 的价格是0.5元，那么他对商品x的需求价格弹性是未知类型：{'options': ['-10', '- 1/5', '-1/10', '\xa0- 1/3'], 'type': 102}