Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated lines
1. y = x^ 1/2 , y = 0 , x = 4
a) the x-axis
b) the y-axis
c) the line x = 4
d) the line x = 6
2. y = x ^ 2 , y = 4x - x^ 2
a) the x-axis
b) the line y = 6
Integration
2007-02-14 7:18 am
回答 (2)
2007-02-14 6:09 pm
✔ 最佳答案
1) The diagram is shown as follows:圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Revvol1.jpg
【此圖乃本人自製圖片，未經本人同意勿擅自連結或使用】
According to the 4 parts required from the question:
(a) → Rotating the light blue region about the x-axis.
(b) → Rotating the white region about the y-axis.
(c) → Rotating the light blue region about the line x = 4.
(d) → Rotating the light blue and yellow regions about the line x = 6.
Therefore,
圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Revvol3.jpg
圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Revvol4.jpg
2) The diagram is shown as follows:
圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Revvol2.jpg
【此圖乃本人自製圖片，未經本人同意勿擅自連結或使用】
First of all, the points of intersection between the cirves are (0,0) and (2,4).
Therefore,
圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Revvol5.jpg
參考: My Maths knowledge
2007-02-16 9:04 pm
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