Question:

How do I integrate Cos x Sin x dx?

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How do I integrate Cos x Sin x dx? I'm working on an engineering problem and having trouble getting up to speed with simple integral calculus. Any help is much appreciated!

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5 ANSWERS


  1. CosXSinS is as simplified as it gets.


  2. cos(x)*sin(x)=1/2 *sin(2x)=>

    int(cosx*sinx*dx)=int(1/2*sin(2x)dx)

    =-1/4*cos(2x)

  3. since

    dy/dx (cos x) = - sin x

    dy/dx (sin x) = cos x

    then integrating them wld be the opp of it.

    integral of Cos x = sin x

    Integral of Sin x = - cos x

    Integral of Cos x Sin x

    = Integral of Cos x + integral of Sin x

    = Sin x - cos x

  4. ∫cosx sinx dx

    = ∫sinx dsinx

    = (1/2)sin^2(x) + c

  5. you can solve in different ways you will get diff answer but they will be right

    1)    put sinx   = t

                 cosxdx  = dt

          

                Ã¢ÂˆÂ« tdt   = t^2/2  +c   =  1/2sin^2 X  +c

    2)    sinxcosx  = 1/2  sin2x  

             ∫ 1/2sin2x  dx   = -1/4  cos2x  +c

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