[微積] 請教高手 double integrals in polar coordinates
在G.zill工數中9.11double integral in polar coordinates EX3如下
find the volume of the solid that is under the hemisphere
z=sqrt(1-x^2-y^2) and above the region bounded by the graph
of the circle x^2+y^2-y=0
此題作者用polar coordinate轉換去做
π/2 sinθ 1/2
= 2∫ ∫ (1-r^2) r drdθ=.....=π/3-4/9
0 0
但問題來了 作者在最後remarks
However, carry out the iterated integration
π sinθ 1/2
=∫ ∫ (1-r^2) r drdθ=π/3
0 0
and see if the incorrect π/3. What goes wrong ?
為何明明是對稱圖形卻不可以這麼做ㄋ?
我卡在這裡好久了請各位高手幫幫我
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03/10 11:52, , 1F
03/10 11:52, 1F