微積分之triple integration!

Question

圖片參考：http://lh3.ggpht.com/_EFBhGexSOmE/TBiUtHEed5I/AAAA...

http://lh3.ggpht.com/_EFBhGexSOmE/TBiUtHEed5I/AAAA...

Answer 1

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z的積分區間沒有根號耶

直接用球座標轉換

原式=∫∫(9-x^2-y^2)√(x^2+y^2) dxdy, x=rcosθ, y=rsinθ

=∫∫(9-r^2)r rdrdθ, r:[0,3], θ:[0,pi]

=∫∫(9r^2-r^4) drdθ

={3r^3-(1/5)r^5|[0,3]}{θ|[0,pi]}

=162pi/5

2010-06-17 08:31:39 補充：

應該是圓座標轉換