Consider the plane region bounded by the graph of
(x/a)^2+(y/b)^2=1
where a>0 b>0 show that the volume of the ellipsoid
formed when this region about the y-axis is 4/3˙Pi˙a^2˙b
我用SHELL做
切成跟Y軸垂直的長方條
R(y)=x=a√{1-(y/b)^2}
0
v= 2Pi∫ a√{1-(y/b)^2}˙y dy
b
最後的結果= 2/3˙Pi˙a˙b^2
可是解答是4/3˙Pi˙a^2˙b
解答是切成跟Y軸平行的長方條
實在看不懂自己哪邊錯了
解答的列式
0
v=2(2Pi)∫ b√{1-(x/a)^2}˙x dx
b
體積為什麼還多乘2倍?不是只繞Y軸轉嗎?
先謝謝幫我解答的高手
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