作者nady32 (nady)
看板trans_math
标题Re: [考古] 96学年度元智大学转学考题
时间Sat Apr 24 22:39:32 2010
※ 引述《gs86137 (小飞鱼)》之铭言：
: Use the disk or shell method to find the volume of the solid generated
: by revolving the region bounded by the graphs of the equations
: x^2/3 + y^2/3 = 3^2/3 about the given line
: (a)the x-axis
: (b)the y-axis
: 有请神人~~
另x=3cos^3 t
y=3sin^3 t
3 0
V=2∫pi y^2dx=2∫ pi(3sin^3t)^2d(cos^3t)
0 pi/2
pi/2
=2pi 3^3∫ (3sin^7t-3sin^9t)dt
0
=162pi(6*4*2/7*5*3*1 -8*6*4*2/9*7*5*3*1)=(288/35)pi
对Y轴也是这样解
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