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Math Help - Improper integrals:

  1. #1
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    Improper integrals:

    \int_{\frac{1}{2}}^{2} \frac{dz}{z(ln{z})^{\frac{1}{5}}}

    so:

    \lim{t\to{1^{-}}} \int_{\frac{1}{2}}^{t} {\frac{dz}{z(ln{z})^{\frac{1}{5}}} + \lim{t\to{1^{+}}}\int_{t}^{2}\frac{dz}{z(ln{z})^{\  frac{1}{5}}}


    \lim{t\to 1^{-}} \frac{5}{4} (ln{z})^{\frac{4}{5}}\big|_{\frac{1}{2}}^{t} + \lim{t\to 1^{+}} \frac{5}{4} (ln{z})^{\frac{4}{5}}

    when i evaluate this.... the answer doesnt appear to be the sam as the back of book:
    Answer at back of book : 0]

    Edit:
    kindly delete this thread for double posting its because of lagging
    Last edited by ^_^Engineer_Adam^_^; September 6th 2007 at 04:18 AM.
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  2. #2
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    When I evaluated the integral in Mathematica 6 I got an imaginary solution so if the book was looking for real solutions you might have mistaken a null set (zero with a line through it) for a zero. Below is the answer mathematica gave me.. Hope this helps

    1.6866 -0.548011


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  3. #3
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    Quote Originally Posted by jandrewross View Post
    When I evaluated the integral in Mathematica 6 I got an imaginary solution so if the book was looking for real solutions you might have mistaken a null set (zero with a line through it) for a zero. Below is the answer mathematica gave me.. Hope this helps

    1.6866 -0.548011
    This problem was answered in another thread (apparently you missed Engineer_Adam's last comment.)

    I should mention that he is taking z to be a real variable here, not a complex one, as you can see by the limits so the value of the integral must be real.

    -Dan
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