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
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