※ 引述《JukeFF (JukeFF)》之銘言：
: 想請問一下 如下圖https://i.imgur.com/VMGlKFW.jpg
: 我怎麼算都是負數
: 先畫出圖之後
: 求出體積 y=根號x x=根號y
: 帶人二重積分 怎麼算都不對..
: 求神人解答...
x = y^2
y = x^2
交點在(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
過程是這樣
答案你字幾再驗算看看