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Math Help - integrate using substitution x = 2sec@

  1. #1
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    Talking integrate using substitution x = 2sec@

    Integrate
    sqrt (x^2 -4) using the substitution x = 2sec@

    I had:

    x = 2sec@
    dx = 2sec@tan@

    sqrt (4sec^2 @ -4) x 2sec@tan@ d@
    = 4tan^2 @ sec@

    and now I'm stuck.

    Thanks
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  2. #2
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    Quote Originally Posted by differentiate View Post
    Integrate
    sqrt (x^2 -4) using the substitution x = 2sec@

    I had:

    x = 2sec@
    dx = 2sec@tan@

    sqrt (4sec^2 @ -4) x 2sec@tan@ d@
    = 4tan^2 @ sec@

    and now I'm stuck.

    Thanks
    Ted had written answer before I did. So I deleted mine. Anyway this integration could be easily done if you use x=2sin@.

    Hope this helps you.
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  3. #3
    Ted
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    Quote Originally Posted by differentiate View Post
    Integrate
    sqrt (x^2 -4) using the substitution x = 2sec@

    I had:

    x = 2sec@
    dx = 2sec@tan@

    sqrt (4sec^2 @ -4) x 2sec@tan@ d@
    = 4tan^2 @ sec@

    and now I'm stuck.

    Thanks

    \int tan^2(\theta) sec(\theta) \, d\theta=\int (sec^2(\theta)-1)sec(\theta) \, d\theta=\int sec^3(\theta) \, d\theta - \int sec(\theta) \, d\theta

    the first one is a well-known integral and you should know how to integrate the second one
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