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 Forum » EDUCATION » MATHEMATICS » Integrate CosxSinx dx use three different methods
Integrate CosxSinx dx use three different methods
seifDate: Tuesday, 11/Jun/2013, 10:44 | Message # 1
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IntegrateCosxSinx dx use three different methods. I only know one method .... can anyone help me about other topics?

Yes I can

AdminDate: Tuesday, 11/Jun/2013, 10:46 | Message # 2
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First Method:
Int, CosxSinx dx                     let U = Sinx ------>      du/dx = Cosx       then      dx = du/Cosx
Int, Cosx  U (du/Cosx)           hapo Cosxitaondoka na Cosx iliyopo ndani ya Bracket
Int, U du
= ½ U2 + C                          C is constant.
Since U = Sin x then:
=1/2Sin2x +C

Second Method:
Int, CosxSinx dx               let U = Cosx ------>      du/dx = -Sinx      then   dx = du/-Sinx
Int, U Sinx (du/-Sinx)       hapo Sinx itaondoka na Sinx iliyopo ndani ya Bracket.)
Int, -U du
= -½ U2 + C                   C is constant.
Since U = Cos x then:
=-1/2 Cos2x +C              NOTE: Be careful withNegative Sign

Third Method:
Remember that sin2x= 2SinxCosx  so by dividing by 2 bothsides we obtain1/2Sin2x = SinxCosx
Therefore: CosxSinx= 1/2Sin2x then integrate now 1/2Sin2x. this is the third method:

Int, 1/2Sin2x                           let U = 2x ------>      du/dx = 2      then   dx = du/2
Int, 1/2SinU X du/2
Int, 1/4SinU du
= -1/4CosU + C                      But U = 2x
Therefore:
=-1/4Cos2x +C

 Forum » EDUCATION » MATHEMATICS » Integrate CosxSinx dx use three different methods
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