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Math Help - [SOLVED] improper integral

  1. #1
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    [SOLVED] improper integral

    question: \int_{-\infty}^{-1} \frac{1}{\sqrt{2-w}}dw
    work: \lim_{t\to-\infty}\int_t^{-1}\frac{1}{\sqrt{2-w}} \, dw I used u substitution with u=2-w leaving me with \lim_{t\to-\infty}2\sqrt{2-w} from -1 to t
    answer: diverges. Sorry, delete this post
    Last edited by mr fantastic; July 22nd 2009 at 11:49 PM. Reason: Fixed latex, tried to make the post more intelligible.
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    Quote Originally Posted by superdude View Post
    question: \int_{-\infty}^{-1} \frac{1}{\sqrt{2-w}}dw
    \int \frac{1}{\sqrt{2-w}}dw = -2 \sqrt{2-w}

    So evaluated as a definite integral between - \infty and -1 the integral does not converge.
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  3. #3
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    Quote Originally Posted by superdude View Post
    question: \int_{-\infty}^{-1} \frac{1}{\sqrt{2-w}}dw
    work: \lim_{t\to-\infty}\int_t^{-1}\frac{1}{\sqrt{2-w}} \, dw I used u substitution with u=2-w leaving me with \lim_{t\to-\infty}2\sqrt{2-w} from -1 to t
    answer: diverges. Sorry, delete this post
    Once a reply has been given to a question it is policy not to delete the thread.
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