※ 引述《sampo123 (ask)》之銘言：
: Please use both triple and double integral to find
: the volume of the solid bounded by x^2 + y^2 +z =1,
: xy,yz,and xz plane in the first octant.
double integral
V = ∫∫ zdxdy
π/2 1 2
= ∫ ∫ ( 1- r) rdrdΘ
0 0
1 2
=( π/2) ∫ ( 1- r ) rdr = π/8
0
triple integral
V = ∫∫∫ 1 dV 2
(π/2) 1 1-r
= ∫ ∫ ∫ 1*rdzdrdΘ
0 0 0
(π/2) 1 2
= ∫ dΘ ∫ ( 1- r ) rdr =( π/2)*1/4 = π/8
0 0
不知道有沒有錯
參考看看八
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※ 編輯: youyouyou 來自: 140.115.213.118 (03/01 14:52)