clementf2b

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.

數痴夢王

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 ]

數痴夢王

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 ]