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Math Help - Which is correct ?

  1. #1
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    Which is correct ?

    Hi.

    (Let, Int=integral and Sqrt=square root and In=natural log)

    In a math book I found that

    Int( Sqrt(Z^2-A^2) )
    = (A^2)/2 * ( (Z*Sqrt(Z^2-A^2))/(A^2) - In((Z+sqrt(z^2-A^2))/A) )
    = (Z*Sqrt(Z^2-A^2))/2 - ( (A^2)/2 * In((Z+sqrt(z^2-A^2))/A) )

    but with my TI-89 titanium calculator the same integral gave

    Int( Sqrt(Z^2-A^2) )
    = (Z*Sqrt(Z^2-A^2))/2 - ( (A^2)/2 * In(Z+sqrt(z^2-A^2)) )

    After some working out on paper, I found my calculator gave the wrong result. I not too sure why this is. Can anyone tell me which is correct ?

    Thanks
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  2. #2
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    Which variable is this respect to?

    \int \sqrt{z^2-a^2}da is much different from \int \sqrt{z^2-a^2}dz

    Jameson
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  3. #3
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    You can check an alleged indefinite integral (anti-derivative) by differentiating ...
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  4. #4
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    ah... sorry, it's with repect to z.

    thanks
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  5. #5
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    \int \sqrt{x^2-a^2}dx=\frac{x\sqrt{x^2-a^2}}{2}-\frac{a^2\ln(x+\sqrt{x^2-a^2})}{2}
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