How to do this?

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  1. sabre2th1's Avatar
    1 17-06-2012  12:08
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    How to do this?


    Any way to do this using the methods in the C4 edexcel book?
  2. latentcorpse's Avatar
    2 17-06-2012  12:38
    • Peer Of The TSR Realm
    Re: How to do this?
    (Original post by sabre2th1)


    Any way to do this using the methods in the C4 edexcel book?
    use a trig identity to get

    \frac{1}{2} \int \frac{dx}{\sin^2{2x}}=\frac{1}{2 } \int \frac{dx}{\mathrm{cosec}^2{2x}}

    Now, use quotient rule to show that \frac{d}{dx} (\cot{2x}) = -2 \mathrm{cosec}^2{2x}

    From there, it should be obvious....
    Last edited by latentcorpse; 17-06-2012 at 12:39.
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  3. TenOfThem's Avatar
    3 17-06-2012  14:53
    • No --- I am a Newbie --- Honest
    Re: How to do this?
    (Original post by latentcorpse)
    use a trig identity to get

    \frac{1}{2} \int \frac{dx}{\sin^2{2x}}=\frac{1}{2 } \int \frac{dx}{\mathrm{cosec}^2{2x}}

    Now, use quotient rule to show that \frac{d}{dx} (\cot{2x}) = -2 \mathrm{cosec}^2{2x}

    From there, it should be obvious....

    When you changed to cosec you did not mean to put 1/it
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  4. sabre2th1's Avatar
    4 17-06-2012  18:46
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    Re: How to do this?
    (Original post by latentcorpse)
    use a trig identity to get

    \frac{1}{2} \int \frac{dx}{\sin^2{2x}}=\frac{1}{2 } \int \frac{dx}{\mathrm{cosec}^2{2x}}

    Now, use quotient rule to show that \frac{d}{dx} (\cot{2x}) = -2 \mathrm{cosec}^2{2x}

    From there, it should be obvious....

    (Original post by TenOfThem)
    When you changed to cosec you did not mean to put 1/it
    I've got it I think:

    Cos 2x = 1-2Sin2x

    therefore Cos 4x = 1-2Sin22x

    therefore 1-Cos4x = 2Sin22x

    therefore 1/(2Sin22x) = 2(cosec22x)

    the integral of 2(cosec22x) = -4cot2x

    Is the above right?
    Last edited by sabre2th1; 17-06-2012 at 18:51.
  5. TenOfThem's Avatar
    5 17-06-2012  18:50
    • No --- I am a Newbie --- Honest
    Re: How to do this?
    (Original post by sabre2th1)
    I've got it I think:

    Cos 2x = 1-2Sin2x

    therefore Cos 4x = 1-2Sin22x

    therefore 1-Cos4x = 2Sin22x

    therefore 1/(2Sin22x) = 2(cosec22x)

    the integral of 2(cosec22x) = -2cot2x

    Is the above right?
    You have 2 when it should be 1/2
  6. sabre2th1's Avatar
    6 17-06-2012  19:01
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    Re: How to do this?
    (Original post by TenOfThem)
    You have 2 when it should be 1/2
    Where? (I edited it several times in a row, so I might have corrected it just after you posted)

    Thanks
  7. TenOfThem's Avatar
    7 17-06-2012  19:10
    • No --- I am a Newbie --- Honest
    Re: How to do this?
    (Original post by sabre2th1)
    Where? (I edited it several times in a row, so I might have corrected it just after you posted)

    Thanks
    \frac{1}{2sin} = \frac{1}{2}cosec
  8. sabre2th1's Avatar
    8 17-06-2012  19:11
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    • Location: Southampton
    • Posts: 1,048
    Re: How to do this?
    (Original post by TenOfThem)
    \frac{1}{2sin} = \frac{1}{2}cosec
    Oh! I can spot it now! Thanks
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