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¼ÐÃD: [¾Ç³N±´°Q] M2 Integration°Ý¼Æ [¥´¦L¥»­¶]

§@ªÌ: kimwong3252000    ®É¶¡: 2012-3-18 12:57     ¼ÐÃD: M2 Integration°Ý¼Æ

Find the volume of the solid of revolution generated by revolving the shaded region, where the "arrow" indicates the axis of revolution



Answer:


µª©¥½ç°s
§@ªÌ: ¬P°¨    ®É¶¡: 2012-3-18 13:02

amath ªº §Ú¦­´N§Ñ¤F(Àq)
§@ªÌ: UniCorn    ®É¶¡: 2012-3-18 13:12

³oÃþÃD¥Ø³£«Ü²³æ§a...
±o3ºØ¤èªk¤SµLtrick
(¬Ý§¹°°ª«¦Aµª...
§@ªÌ: kimwong3252000    ®É¶¡: 2012-3-18 13:12



QUOTE:
­ì©«¥Ñ UniCorn ©ó 2012-3-18 13:12 µoªí
³oÃþÃD¥Ø³£«Ü²³æ§a...
±o3ºØ¤èªk¤SµLtrick

­p·¥³£­p­ø¨ì- -

©Ò¥H¥ý°Ý§A¦a
§@ªÌ: ¬P°¨    ®É¶¡: 2012-3-18 13:17



QUOTE:
­ì©«¥Ñ kimwong3252000 ©ó 2012-3-18 13:12 µoªí

­p·¥³£­p­ø¨ì- -

©Ò¥H¥ý°Ý§A¦a

- -¥i¥H §â®Ñ¤¤¦³Ãöªº­¶¼Æ¤W¸ü¶Ü-.-?
§@ªÌ: kimwong3252000    ®É¶¡: 2012-3-18 13:21



QUOTE:
­ì©«¥Ñ ¬P°¨ ©ó 2012-3-18 13:17 µoªí

- -¥i¥H §â®Ñ¤¤¦³Ãöªº­¶¼Æ¤W¸ü¶Ü-.-?



§@ªÌ: ¬P°¨    ®É¶¡: 2012-3-18 13:27

-.-¤U¯u«YËÝin §Ú¥H¬°ËÝin ¿ù
¦pªG«YËÝ
10«}«Y
3.14 s (cosx-1/2)^2 dx
§@ªÌ: ¬P°¨    ®É¶¡: 2012-3-18 13:30

14«Y«}3.14 [s(sin x -4)^2dx-s(2sin x -4)^2dx]?
================================
­p¼Æ §A¦Û¤v°µ³â  ¦pªGÉN¿ùªº¸Ü

[ ¥»©«³Ì«á¥Ñ ¬P°¨ ©ó 2012-3-18 14:12 ½s¿è ]
§@ªÌ: UniCorn    ®É¶¡: 2012-3-18 13:48

ÂI¸Ñ§Ú­Óµª®×­ø¦P§AªG­Ó...
«Y§Ú¿ù©w§A¿ù - -

§@ªÌ: kimwong3252000    ®É¶¡: 2012-3-18 13:49



QUOTE:
­ì©«¥Ñ UniCorn ©ó 2012-3-18 13:48 µoªí
ÂI¸Ñ§Ú­Óµª®×­ø¦P§AªG­Ó...
«Y§Ú¿ù©w§A¿ù - -

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­p­ø¨ì®Ñ­Óanswer

©Ò¥H¥ý°Ý§A¦a
§@ªÌ: UniCorn    ®É¶¡: 2012-3-18 13:56



QUOTE:
­ì©«¥Ñ kimwong3252000 ©ó 2012-3-18 01:49 PM µoªí

§Ú¦P§A­p¨ì¤@¼Ë

­p­ø¨ì®Ñ­Óanswer

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§Ú¥Î¹q¸£In¤@¦¸³£«Y©O­Ó
§@ªÌ: kimwong3252000    ®É¶¡: 2012-3-18 13:59



QUOTE:
­ì©«¥Ñ UniCorn ©ó 2012-3-18 13:56 µoªí

®Ñ­Óµª®×¿ù
§Ú¥Î¹q¸£In¤@¦¸³£«Y©O­Ó

ËÝ14©O?
§@ªÌ: UniCorn    ®É¶¡: 2012-3-18 14:04



QUOTE:
­ì©«¥Ñ kimwong3252000 ©ó 2012-3-18 01:59 PM µoªí

ËÝ14©O?

14啱

§@ªÌ: kimwong3252000    ®É¶¡: 2012-3-18 14:06



QUOTE:
­ì©«¥Ñ UniCorn ©ó 2012-3-18 14:04 µoªí

14啱

­ø¸Ó«{
§@ªÌ: ¬P°¨    ®É¶¡: 2012-3-18 14:09



QUOTE:
­ì©«¥Ñ UniCorn ©ó 2012-3-18 14:04 µoªí

14啱

-.-ÂI¸Ñ«Y4-y ­ø«Yy-4ge?
§@ªÌ: UniCorn    ®É¶¡: 2012-3-18 14:28



QUOTE:
­ì©«¥Ñ ¬P°¨ ©ó 2012-3-18 02:09 PM µoªí

-.-ÂI¸Ñ«Y4-y ­ø«Yy-4ge?

just the same
¤£¹L4-y make sense D
radius «Y­t¼ÆÁ`ı±o©Ç©Çªº
§@ªÌ: ¬P°¨    ®É¶¡: 2012-3-18 14:31



QUOTE:
­ì©«¥Ñ UniCorn ©ó 2012-3-18 14:28 µoªí

just the same
¤£¹L4-y make sense D
radius «Y­t¼ÆÁ`ı±o©Ç©Çªº

¦]¬°§Ú¥Î ·í±ø ½u©Ô¥hx ¶b¨ìÚ» §Úı±o¥Î4-yÚ»¦n©ÇÂû-.-"
§@ªÌ: UniCorn    ®É¶¡: 2012-3-18 14:35



QUOTE:
­ì©«¥Ñ ¬P°¨ ©ó 2012-3-18 02:31 PM µoªí
·í±ø ½u©Ô¥hx ¶b¨ìÚ»

³o¬OÔ£ -.-

In volume ´N¬O§äradius,­ppi r^2 ¦A­¼°ª(dx) §a...
¨º radius ¬O +ve «Ü¥¿±`§a...
§@ªÌ: ¬P°¨    ®É¶¡: 2012-3-18 14:39



QUOTE:
­ì©«¥Ñ UniCorn ©ó 2012-3-18 14:35 µoªí

³o¬OÔ£ -.-

In volume ´N¬O§äradius,­ppi r^2 ¦A­¼°ª(dx) §a...
¨º radius ¬O +ve «Ü¥¿±`§a...

--------------------------------y=4
¦V¤U©Ô
--------------------------------y=0
³o¤£´N¬O y - 4¤F¶Ü-.-?
·í§A¨ìy=0ªº®É­Ô´N¥i¥H¦n©ö­p-.-"
¤£¹L¥ÎrÚ» §A­Ó³£¥¿±` ge
§@ªÌ: UniCorn    ®É¶¡: 2012-3-18 14:44



QUOTE:
­ì©«¥Ñ ¬P°¨ ©ó 2012-3-18 02:39 PM µoªí


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¦V¤U©Ô
--------------------------------y=0
³o¤£´N¬O y - 4¤F¶Ü-.-?
·í§A¨ìy=0ªº®É­Ô´N¥i¥H¦n©ö­p-.-"
¤£¹L¥ÎrÚ» §A­Ó³£¥¿±` ge

¹ï¤£°O equation ªº§Ú¨Ó»¡
shift ¥h­þùاڳ£¥u·|§ä radius...
§@ªÌ: ¬P°¨    ®É¶¡: 2012-3-18 14:45



QUOTE:
­ì©«¥Ñ UniCorn ©ó 2012-3-18 14:44 µoªí

¹ï¤£°O equation ªº§Ú¨Ó»¡
shift ¥h­þùاڳ£¥u·|§ä radius...

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