Re: [微積] 旋轉體表面積
※ 引述《vexchy (樂觀&神秘)》之銘言：
: 2 lnx
: y = 2x - ----- + 19 1≦x ≦e
: 16
: 對y軸旋轉...
: 怎麼改成x = f(y).. 還是說我方向錯了><"? 求救求救
: Find the area of the surface obtained by rotating the curve , about
: (b) the y-axis
Area=∫2πx ds ds=√((dy/dx)^2+1) dx
dy/dx=4x-1/(16x)=(64x^2-1)/(16x)
(dy/dx)^2+1=(4096x^4-128x^2+1)/(256x^2) + 1
=(4096x^4+128x^2+1)/(256x^2)
=((64x^2+1)/(16x))^2
So, Area=∫2πx ds
e 64x^2+1
=2π∫x‧------- dx
1 16x
π 64x^3 |e
=---(-----+x)|
8 3 |1
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