作者Honor1984 (奈何上天造化弄人？)
看板trans_math
标题Re: [积分] 二重积分疑问
时间Wed May 9 00:28:24 2018
※ 引述《JukeFF (JukeFF)》之铭言：
: 想请问一下 如下图https://i.imgur.com/VMGlKFW.jpg
: 我怎麽算都是负数
: 先画出图之後
: 求出体积 y=根号x x=根号y
: 带人二重积分 怎麽算都不对..
: 求神人解答...
x = y^2
y = x^2
交点在(x - y) = -(x - y)(x + y)
=> (x - y)(1 + x + y) = 0
=> x = 0, 1
或x^4 = y^2 = x
=> x(x - 1)(1 + x + x^2) = 0
=> x = 0, 1
S (x^2 + y)dx dy
x = √y
= S ((1/3)x^3 + xy)| dy
x = y^2
1
= S (1/3)[y√y - y^6] + [y√y - y^3] dy
0
= (8/15) - (1/21) - (1/4)
= 33/140
过程是这样
答案你字几再验算看看
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1F：推 JukeFF : 谢谢! 05/10 01:06