应用极坐标变换,求下面曲面所界立体的体积:[tex=4.071x1.286]VVTh7UI8ynwoNBTduSiHUg==[/tex],[tex=5.5x1.429]+jUY+deWL6iVXIS7VWREf8VHYJNbQ2mPY2Frw4yf5v4uOVAawZMeI9I9URG59fxN[/tex][tex=1.571x1.286]Za3o+QQVbLth3yDEMEc9Mg==[/tex],[tex=2.286x1.286]JLs9PeQldj+slOTItz+PvA==[/tex]([tex=2.357x1.286]W6+jNfDjkvQb4nWE+47z2g==[/tex],[tex=2.357x1.286]cyLpros3NFCEwVSzDDR9cQ==[/tex]).

2022-07-01

应用极坐标变换,求下面曲面所界立体的体积:[tex=4.071x1.286]VVTh7UI8ynwoNBTduSiHUg==[/tex],[tex=5.5x1.429]+jUY+deWL6iVXIS7VWREf8VHYJNbQ2mPY2Frw4yf5v4uOVAawZMeI9I9URG59fxN[/tex][tex=1.571x1.286]Za3o+QQVbLth3yDEMEc9Mg==[/tex],[tex=2.286x1.286]JLs9PeQldj+slOTItz+PvA==[/tex]([tex=2.357x1.286]W6+jNfDjkvQb4nWE+47z2g==[/tex],[tex=2.357x1.286]cyLpros3NFCEwVSzDDR9cQ==[/tex]).

答案：

解:极坐标变换[tex=3.286x1.286]jBUla9HZ7SQ+s+cx2FCrkw==[/tex][tex=6.5x1.286]vVL0EYMm10NF6Ro5aUF8Ccb9Eiu1NUr7Hj7s5UkPZvEx7gSQj18KxP9I9ZgjNhst[/tex],[tex=4.857x2.286]V9fVXReHUrcmKJSTnoNlS9kETbtpIdm/4BHsh0C2rAElichcOe3KTg438qj/xkR1a33wv6B4NjrtmEgGlBbR7g==[/tex].曲线[tex=5.5x1.429]+jUY+deWL6iVXIS7VWREf8VHYJNbQ2mPY2Frw4yf5v4uOVAawZMeI9I9URG59fxN[/tex][tex=1.571x1.286]Za3o+QQVbLth3yDEMEc9Mg==[/tex]的极坐标方程为[tex=8.143x1.286]YYYYtqYyV5Pg/nnxj1iqZ7spz7unxwJrL3c8/vfStS99WddcpYfVyJY3CzX+I1CD[/tex][tex=2.5x1.286]jy21h0p+z5riu+53/tFw/zJYdaagEMxjbL5A2km68EE=[/tex].[tex=1.643x1.0]JA/NNmYzHtRC+PvvyWsJDQ==[/tex][tex=10.929x3.5]qJCV9oMuCSSbqVGRrFO0fi9tynPsWR7WsGJpcKlcSKbhMz51kHTOAFxSLcseUXAQROnkMEKegJJxzQOKKOzLv3BI2he2q1Ll/2O7VvQmMgaZTduuYKH5jo8ZJUSVSR13yakMhmtF/3O9wktWA0sHCtB7yMqSzkoIFPu/MvjytVo=[/tex][tex=15.857x2.5]4Eb9o622d0kgABgzY82+EE2KLHR5G0bbealCOiFdLa52uKfUPVzQx/xQmpv8fDHS1bZjs3A7grkx/4kBfonW0hpcRKOHK/M5iDFvuqB/yNgKnCSEc5RgYU8P+wF1HItn3dAKzMbz2fFspgNZ0pMKlQ==[/tex][tex=14.571x2.5]gZ6HzPiok05f2eMnMBndQzkBrrRG0q4FQeWHMutzBRvJQvm/PdPze45pOTd5FDyUCcyzgYqx2hxE7QSWk+NLEWKjlcxnxcah2d133jzJkj/xQonECzttfADBYf2VptElqEusFS/SugAWkBDBtlqy/w==[/tex][tex=10.429x2.5]iUezZQMktnbUx8xAD2w3NMfQ98UyWobb8TGk3yA3LbJ8wmZ+/BfjHlGcnX0ZoG3a2D+jRGqfdqKX0PrgDSIH1oXUMetkwUNKs3loFwIOHQWidE0vWtC+XoUTtdKVIOA05tD+EFQqvHjvnVWb6cF19A==[/tex][tex=8.0x1.357]5PlGpk6u8yzp8ck4oiJRqiUC83j4dVHFrg9AqGzSTBJx+hXvi700osGb2gV68urU6iQEN+OO8mB2zcV6eGfKMPWZ4m/EPFDb2AiNj5aRHbk=[/tex][tex=11.643x2.5]NRvq7O5zqxtvs45LntRSiz0luhYwR75VPMAMvuVPT0O3MsSLXE8MbIgLdQNr9LBZMOzvN45Zg0w5pxpboQWn9v48FOh/auiUwYxlTzQ0b0M4iNmrESett6qCNmrF3nJ2eN/7EH0Ok8dwcwMMH6iV/eBiTSIMBDGzRcAc/T3qzmA=[/tex][tex=7.929x2.5]iUezZQMktnbUx8xAD2w3NLKKVmARkrmnkktD+PlKHSVDLvgCJhb/XwYjOh03gXEvhWtxTyC3rSH43b672NmrnD4FE0cX7U5l+CQAxR/CQdCR8Xe2wkiLCrIzxl7OF96a[/tex][tex=9.643x2.214]iUezZQMktnbUx8xAD2w3NFG+QpMG4vzwb9EgfwDYhPGtnApouhYYoRVp5pvV+eotl4wsfX6sWcv5/QQy8YdClxXAvCX4eAdwHRon7CDyqHgP3LNphAgOP4aeVsqRFeMJlW4btoFZpnrNxcylSU8yYQ==[/tex][tex=6.571x2.5]krdBX1id32PVCJ1DKJhiCc9lGe/8lKdXhwdNHOGrgZngcVSTKRZ+jVJHuvxQyoYCCRGkp7PoZTBWLD6mMwHQLc3IpMa3lZ3mTGCzLW7RBa4=[/tex].

举一反三

内容

0
求由四个平面[tex=2.357x1.286]F20DA9b5PZyvxJH27l4LOQ==[/tex]，[tex=2.357x1.286]+lfyPLkaB2aZzha73p3Bvg==[/tex]，[tex=2.357x1.286]jgIRiGqlkdCMqO92sJAASg==[/tex]及[tex=2.286x1.286]00XlJXnsFPYY5douG8n+zA==[/tex]所围成的柱体被平面[tex=2.286x1.286]JLs9PeQldj+slOTItz+PvA==[/tex]与[tex=6.714x1.286]hlSBzy/xHLZhrxsmPbKGq0tueyYBb65zitXHpsLWa5c=[/tex]截得的立体体积 .
1
计算由四个平面[tex=2.357x1.286]F20DA9b5PZyvxJH27l4LOQ==[/tex]，[tex=2.357x1.286]+lfyPLkaB2aZzha73p3Bvg==[/tex]，[tex=2.357x1.286]jgIRiGqlkdCMqO92sJAASg==[/tex]，[tex=2.286x1.286]00XlJXnsFPYY5douG8n+zA==[/tex]所围成的柱体被平面[tex=2.286x1.286]JLs9PeQldj+slOTItz+PvA==[/tex]及[tex=6.714x1.286]/IM4BpXrl6LFoB+hKPdGUg==[/tex]截得的立体的体积。
2
化三重积分[tex=9.0x2.786]42gBN9Krru//PFOqkQbPVoHpcXfHmBRej9ues2hAjo/79EcVaGYsH+QLShXClqBv52Vwm3UQIVHeYkWy/B6yzp17Gi6Y8jI/+FVEHQHPV9A=[/tex]为三次积分，其中积分区域[tex=0.714x1.286]1YkIdjxXLHdjdjLEO+eusQ==[/tex]分别是：（1）由[tex=2.857x1.286]zll590W/Ueri9LhcpUaNXA==[/tex]，[tex=4.071x1.286]b+IRDFXmDzDdHpS9UW05nA==[/tex]，[tex=2.286x1.286]JLs9PeQldj+slOTItz+PvA==[/tex]所围成的闭区域；（2）由六个平面[tex=2.357x1.286]F20DA9b5PZyvxJH27l4LOQ==[/tex]，[tex=2.357x1.286]DbxZR1Yb806Oy0xU84fgow==[/tex]，[tex=2.286x1.286]00XlJXnsFPYY5douG8n+zA==[/tex]，[tex=4.571x1.286]1XpLXdWMqvn2kxHEIhh81A==[/tex]，[tex=2.357x1.286]NFij4XQM3i2GDItyYXv86Q==[/tex]，[tex=2.286x1.286]hW5Ac29gcX2YJno8Ypzqmw==[/tex]所围成的闭区域；（3）由曲面[tex=5.357x1.286]Z1Pc7IunBToCiM+w0aWebdzhX98zYuPfIYMCFXSfjcs=[/tex]及[tex=4.429x1.286]S+o4p4JbnFJBiJwKNosoTQ==[/tex]所围成的闭区域。
3
流体流速 [tex=6.571x1.286]0xbOPrVrSMKcudg3NAts7uR/d7oYcOZ7U/x7TWieHqYUK9KJgFmujDO+IrS49pAr[/tex] 求单位时间内穿过 [tex=0.714x2.0]8oX8VJMvV0WppJIc2wifleVrlgtfhiI9iXYh1rswxyc=[/tex] 球面 [tex=3.929x1.286]OgRXGBnuYUkrpNulxRW68D36NV9X5hevhTpuCfbJIg4=[/tex][tex=2.714x1.286]hLb6zbJazzCJ8AJyZnfHlQ==[/tex] ([tex=2.357x1.286]W6+jNfDjkvQb4nWE+47z2g==[/tex], [tex=2.357x1.286]cyLpros3NFCEwVSzDDR9cQ==[/tex], [tex=2.286x1.286]5t/j3K+l3DXv8ylrB5Zq1w==[/tex]) 的流量.
4
求由平面 [tex=2.357x1.286]F20DA9b5PZyvxJH27l4LOQ==[/tex], [tex=2.357x1.286]+lfyPLkaB2aZzha73p3Bvg==[/tex], [tex=2.286x1.286]JLs9PeQldj+slOTItz+PvA==[/tex] 及 [tex=4.0x1.286]Y2PAOcQLlnse9p/I1rNCIQ==[/tex] 与椭圆抛物面 [tex=3.0x1.286]yFFuWBktvEIXQBePtMKHkQ==[/tex][tex=3.143x1.286]1MrHNO42U0UB36xVB0mfqlSGMDXCIKuU0KvWlcvpOP4=[/tex] 围成的立体的体积.