Re: [微積] 微積分面積問題
※ 引述《bahamut5461 (永澤)》之銘言：
: ※ [本文轉錄自 Math 看板 #1E9krASa ]
: 作者: bahamut5461 (永澤) 看板: Math
: 標題: [微積] 微積分面積問題
: 時間: Wed Jul 20 22:59:18 2011
: Consider the region D bounded by y = 1, y = x^2, x = 1 and y-axis.
: (a) Find the volume generated by rotating the region D about x-axis.
shell method
dV=2πrh dr
=2πy(1-x) dy (y=x^2 dy=2xdx)
=4π(x^2)(1-x) xdx
1
V=4π∫x^3-x^4 dx=4π(1/4-1/5)=π/5
0
: (b) Find the volume generated by rotating the region D about x = -1.
: Please solve the problem. Thanks.
dV=2πrh dr
=2π(1+x)y dx
=2π(1+x)x^2 dx
1
V=2π∫x^2+x^3 dx=2π(1/3+1/4)=7π/6
有錯請告知 謝謝
0
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