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標題: [M2] Problem about Volume through Integration [打印本頁]

作者: clementf2b    時間: 2016-2-21 06:38 PM     標題: Problem about Volume through Integration

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.
y=(x−1)^(1/2) , y=0 , x=5 ;
about the line y=6.


Please give me some helps.Thank You.
作者: 數痴夢王    時間: 2016-3-14 07:53 AM

1. 繪畫圖出來看看

[ 本帖最後由 數痴夢王 於 2016-3-24 12:56 PM 編輯 ]
作者: 數痴夢王    時間: 2016-3-24 01:00 PM

Volume = pi * integrate from 1 to 5 [ 6^2 - (sqrt(x-1)-6)^2] dx
= pi * integrate from 1 to 5 [ 12sqrt(x-1)- (x-1)] dx= pi * [ 8(x-1)^(3/2)- (x-1)^2/2] at x=5
= 56 pi

[ 本帖最後由 數痴夢王 於 2016-4-3 02:22 PM 編輯 ]




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