E-Storeintegration
15 Jan 2008 22:28:37 IST
integration
There is a general method to find integration of sin 9x / sin x , sin 11x/ sin x etc.
we know,
[ ]
[ ] sinx dx / sin x = x + C
[ ][ ] sin 3x dx / sin x = x + sin 2x + C
[ ][ ] sin 5x dx / sin x = x + sin 2x + sin 4x / 4 + C
therefore,
[ ][ ] sin 7x dx / sin x = x + sin 2x + sin 4x / 2 + sin 6x / 3 + C
in this method, we can find integration of sin 9x / sin x , sin 11x/ sin x etc.
( courtesy : Chakrapani Dutta, my friend )
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P90
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Joined: 27 Aug 2007 14:35:10 IST
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15 Jan 2008 23:03:22 IST
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great!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
19 Jan 2008 22:01:43 IST
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again chakrapani dutta did wonder , though with a bit of my help this time
pattern of indefinite integration for sin 2nx/ sin x
sin 2x/ sin x = 2 [ sin x] + C
sin 4x/ sin x = 2[ sin x + (sin 3x) / 3 ] + c
sin 6x/ sin x = 2[ sin x + (sin 3x) / 3 + (sin 5x) / 5] + c
in this way we can integrate even sin10x/sinx, sin 12x/sinx, etc. the value of
sin 10x/ sin x = 2[ sin x + (sin 3x) / 3 + (sin 5x) / 5 + (sin 7x) / 7 + (sin9x) / 9] + c
pattern of indefinite integration for sin 2nx/ sin x
sin 2x/ sin x = 2 [ sin x] + C
sin 4x/ sin x = 2[ sin x + (sin 3x) / 3 ] + c
sin 6x/ sin x = 2[ sin x + (sin 3x) / 3 + (sin 5x) / 5] + c
in this way we can integrate even sin10x/sinx, sin 12x/sinx, etc. the value of
sin 10x/ sin x = 2[ sin x + (sin 3x) / 3 + (sin 5x) / 5 + (sin 7x) / 7 + (sin9x) / 9] + c
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