A combined maths Q

[sameerasadaru]

machala lnSinX anukalanaya karanne kohomada?

 

[nagaya]

sinx walata expansion dala puluwan neda?AL walanm ewa nadda kohedo

 

[sameerasadaru]

bane macho...

 

[Lalakajee]

kotas washayen anukalanaya karanna puluwan neda?? Sure nehe

http://en.wikipedia.org/wiki/Integration_by_parts

http://community.boredofstudies.org/showthread.php/167635-Integration?p=3316947

http://in.answers.yahoo.com/question/index?qid=20080220024624AAoHR5q
me link eke mehema heduwa!!!

I=∫ log(sin x).dx .............eq 1
I=∫logsin(π/2-x)dx
I=∫logcosx dx.......................eq2
add1&2
2I=∫logsinx+logcosx dx
=∫logsinx*cosx dx
=∫log(sin2x)/2 dx
=∫[logsin2x-log2] dx
=∫logsin2xdx - ∫log2dx .................eq 3
in the first integral put 2x=t
d.w.t.x
dx=dt/2
where x=0,t=0 where x=π/2 ,t=π
∫logsint dt with limit t= o & t=π
now
∫logsint dt =2 ∫log sint (dt /2 ) with limit t=0 t=π/2
we can write above eq in "x" also
=2 ∫log sinx (dx/2)
put it in eq 3
2I=2 ∫log sinx (dx/2) - ∫log2dx
but ∫log sinx dx =I
2I= I- ∫log2dx
I= - ∫log2dx with limt x=0& x=π/2
I= -π/2 log2

 

[helo256]

cos(x)/sin(x)

 

[Lalakajee]

http://integrals.wolfram.com/index.jsp?expr=ln%28sinx%29&random=false

 

[sameerasadaru]

kotas walata ba bn.mula ekama aye enawa...

 

[Sachinth]

gunitha suthraya dannawa da

 

[ShanikDJs]

bmp

 

[sameerasadaru]

therenne na bn.anyway Thnkz!!!!!!

 

[Sachinth]

gunitha suthraya dannawada lokka

 

[scooby dooo]

1 bedima sinx vadi kirima cosx

 

[kasuncs]

Machan oke non real parts enawa ekayi karanna bari AL karana ayata.
Mathemtica wage software ekak daagoth karalama balanna puluwan.

 

[scooby dooo]

macho mama dapu vidiha varadida matath hariyata mathaka na,mata mathaka hatiyata ohoma thama

 

[Sachinth]

mathaka widiyatanam mehemai ban

I=∫lnsinxdx u=lnsinx
dv=dx
v=x
du=1/sinx*-cosx

I=uv-∫vdu sammatha suthraya
=lnsinx*x-∫x*-cosx/sinx
=xlnsinx+∫xcotx

∫xcotx tath gunitha suthraya dala balanda ethakota I ta samana kotasak ei ekata I kiyala dala sulu karala I uktha karanda anukala lakuna nathiwa uththaraya ganda I ukthakaranda iri 2 k gahanda

 

[sameerasadaru]

matath meka yaluwek dunne..nikan try karala baluwe.ba bn hadanna....thnk u all!

 

[rehrumesh]

kotas washayen anukalanaya karahan .... mata hariyatama mathaka na karana krame. depaththatama maruwen karala balahan...

 

[kpg]

mata nam Greek wage.terenne nathooooooooo

 

[nagaya]

kotas walata ba bn.mula ekama aye enawa...

mula ekama aye enwanm e deka 2I kiyala ekathu karala aran hadapn balanna

 

[nagaya]

oya samahra ln tiyena ewa AL ayata hadanna ba,apitat issara ohoma prasidda ganak tibba lnsinx wage thama mathaka ekath.samahru wena unge mood upset karanna ohoma ganan denwa,hondama wade clz eke sirgen ahala balana eka,matanm dan athin anukalanaya karanna mathaka na