C4 integration!!

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  1. icouldsay's Avatar
    1 28-05-2012  20:19
    • Junior Member
    • Posts: 34
    C4 integration!!
    Integrating using trig identities.

    I came across this example in my book...

    \int sin^2x dx which is replaced by \int \frac{1}{2}(1-cos2x) dx
    the result is then \frac{1}{2}(x-\frac{1}{2}sin2x) + C
    I don't understand why it is only the bit in the brackets from \int \frac{1}{2}(1-cos2x) dx that gets integrated?
    Is there a step inbetween where \frac{1}{2} is moved before the integral sign? e.g. \frac{1}{2} \int (1-cos2x) dx ?

    Any help is much appreciated!!
  2. ArsLongaVitaBrevis's Avatar
    2 28-05-2012  20:23
    • Banned
    • Location: England
    • Posts: 3,968
    Re: C4 integration!!
    (Original post by icouldsay)
    Integrating using trig identities.

    I came across this example in my book...

    \int sin^2x dx which is replaced by \int \frac{1}{2}(1-cos2x) dx
    the result is then \frac{1}{2}(x-\frac{1}{2}sin2x) + C
    I don't understand why it is only the bit in the brackets from \int \frac{1}{2}(1-cos2x) dx that gets integrated?
    Is there a step inbetween where \frac{1}{2} is moved before the integral sign? e.g. \frac{1}{2} \int (1-cos2x) dx ?

    Any help is much appreciated!!
    Yep - 1/2 is a constant so you can move it outside.
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  3. icouldsay's Avatar
    3 28-05-2012  20:35
    • Junior Member
    • Posts: 34
    Re: C4 integration!!
    Thank you!!
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