作者jjx66os (igor)
看板trans_math
标题[考古] 89清大转考 重积分
时间Sun May 20 13:44:14 2012
Find the volume of the solid T that is bounded above by the cone Z^2=X^2 + Y^2
,below by the x-y plane and on the sides by the hemisphere ___________
Z=√(4-X^2-Y^2)
想问这堤图形是不是一个半圆球在X-Y平面上,然後圆球有一个中空的圆锥呢?
我的解法:
2π 2 _____ ____
∫ ∫ ( √4-r^2 - √r^2 )r drdθ
0 0
但我看书上解答却是:
_
2π √2 _____ ____
∫ ∫ ( √4-r^2 - √r^2 )r drdθ
0 0
我的r上下限是来自hemisphere在X-Y平面上的面积,(Z=0)时,X^2 + Y^2 = 4
请问我哪里弄错了呢?
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※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 61.225.199.170
1F:推 powernba:2X^2+2Y^2=4 没错的话,应该是带这个才对 122.118.252.53 05/20 16:18
2F:→ jjx66os:那...你知道图形长什麽样子吗 61.225.198.115 05/20 22:31
3F:推 powernba:图形应该跟你的描述差不多,只是边界带错 122.118.252.53 05/20 22:45
4F:→ powernba:而已。 122.118.252.53 05/20 22:46
5F:→ jjx66os:了解,很感谢你! 61.225.198.115 05/20 23:15
6F:→ smhead:请问是求圆锥内还是圆锥外、球内?220.136.104.183 05/22 22:37
7F:→ smhead:看到这题我都以为是求半球内、圆锥外的V220.136.104.183 05/22 22:38
8F:→ smhead:如果是你们说得体积,为什麽要提到xy plane220.136.104.183 05/22 22:40
9F:→ smhead:所以我觉得这题他解答也是错得,不知各位220.136.104.183 05/22 22:43
10F:→ smhead:想法如何。好像100中山有一题跟他雷同。220.136.104.183 05/22 22:43
11F:→ smhead:∫∫∫(x^2)zdV 0<=z<=min(√4-r^2-√3r^2)220.136.104.183 05/22 22:51
12F:→ jjx66os:XY平面之上,圆锥外、球内,的体积 吧125.233.248.187 05/24 23:48
13F:→ jjx66os:表示不用算XY平面之下求的体积。125.233.248.187 05/24 23:50
14F:→ smhead:嗯了解 感谢 111.248.155.49 05/30 23:20