Integration by parts.

  1. how would one integrate by parts the following:
    [tex]\int sin^2xdx[/tex]

  2. jcsd
  3. rsm

    rsm 1


    use the fact that sin^2 x = (1-cos2x)/2
    from the formula cos2x=1-2sin^2 x

    Tell me how you wrote that equation
  4. malawi_glenn

    malawi_glenn 4,725
    Science Advisor
    Homework Helper

  5. HallsofIvy

    HallsofIvy 41,270
    Staff Emeritus
    Science Advisor

    Are you required to use integration by parts? As rsm said, there are simple and standard substitutions for [itex]sin^2(x)[/itex] and [itex]cos^2(x)[/itex].

    If you are required to use integration by parts, then, since integration by parts requires a product, the obvious thing to do it write this as a product:
    [tex]\int sin^2(x) dx= \int (sin(x))(sin(x) dx)[/tex]
    Let u= sin(x) and let dv= sin(x) dx. Then du= cos(x)dx and v= -cos(x)
    [tex]\int sin^2 x dx= -sin(x)cos(x)+ \int cos^2(x) dx[/tex]
    Now do the same thing with that integral. Of course, what happens is you will get back to your original [itex]\int sin^2(x) dx[/itex]- but with a lot of other things. Solve that equation algebraically for [itex]\int sin^2(x)dx[/itex]
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