推 Jasonbon:感謝捏~~~~~~~~~~ 59.104.234.11 07/07 20:20
推 Jasonbon:原來簡單到爆=.= 59.104.234.11 07/07 21:53
※ 引述《Jasonbon (秋風掃落葉)》之銘言：
: 7. find the area of surface cut from parabloid x^2 + y^2 - z = 0 by the
: plane z = 2
: 怎麼解呢?
等同於
g:{(x,y)| x^2 +y^2≦2} → R: f(x,y,z)= x^2 + y^2 - z
所對應區域的表面積
= ∫∫√[1+(fx)^2+(fy)^2] dσ
S
= ∫∫√(1+4x^2+4y^2) dxdy
R
轉換為極座標積分即可!
2π √2
= ∫ ∫ r*√(1+4r^2) drdθ
0 0
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