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![[Post New]](/templates/default/images/icon_minipost_new.gif) 16 Mar 2007 02:19:15 IST
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integral of dx / (1 - sin2x) please solve this...................................................................
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16 Mar 2007 02:34:07 IST
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did u try by taking 1 - sin 2x as t ???
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16 Mar 2007 02:37:55 IST
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what will u get by that?
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16 Mar 2007 08:48:05 IST
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convert sin in terms of cos and then use1-cos2x=2sin^2x.
By this you get cosec^x in the numerator and can be integerated into cotx.
Hope you understand............
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Wondering for questions!!!!!!!!!!!!!!! |
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16 Mar 2007 08:51:16 IST
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1 clue write 1 as sin2x+cos2x then u'll get in d denominator as (sinx-cosx)2 or (cosx-sinx)2 now try to solve this.i too will do this. bye.
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Excellence is dedication to a job that is hard to do,going the extramile and always trying to follow through. |
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16 Mar 2007 10:42:03 IST
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sushu is almost right but
dx sin^2 x+cos^2 x
...........................
sinx-cosx
dx (sinx-cosx)^2+sin2x
...............................................
sinx-cosx
dx sinx-cosx+ dx sin2x
.........
sinx-cosx
considering dx sin2x /sinx-cosx
dx (cosx+sinx)^2 -1 / sinx-cosx
by taking
sinx-cosx=t
(cosx+sinx)dx=dt
dx (cosx+sinx)(cosx+sinx)/sinx-cosx -dx/sinx-cosx
hence u can do it from above step onwards
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DO NOT FOLLOW MY WAY.
IT'S TOO DANGER. |
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16 Mar 2007 11:07:53 IST
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hi fren........1 more method
integral of dx/(1-sin2x)
here 1-sin2x can b written as 1-2sinx cosx..........k
now multiply sec^2 x in both num n deno.
so u ll get......integral of sec^2 x dx/(tan^2 x + 1 - 2 tanx)
so........u can write it as....integral of sec^2 x dx/(1-tanx)^2
put tanx = t
n u ll get the answer
hope u got that
: )
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17 Mar 2007 00:13:19 IST
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i am giving one more method:
write sin2x= 2tanx/1+tan(square)x
then solve you will definitely get.
cheers!
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17 Mar 2007 08:16:07 IST
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first of all consider pie i.e 22/7=%(Note this)
now 1-sin2x=1-cos(%/2-2x)
=2sin^2(%/4-x)
now integeral of dx/(2sin^2(%/4-x)
= cosec^2(%/4-x)dx/2
= cot(%/4-x)/2
=(cotx+1)/(cotx-1)2
If anyone likes my reply,do rate it...................
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Wondering for questions!!!!!!!!!!!!!!! |
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22 Mar 2007 21:25:58 IST
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multiply Nr. & Dr. by 1+sin2x i.e. rationalise,u will get the function reduced to sec2x-sec2x.tan2x then apply the formulae & u get the answer
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Don't tell me that a problem is difficult one,if it won't be difficult it would not be a problem. |
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