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Thread: [SOLVED] improper integral

  1. #1
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    [SOLVED] improper integral

    question:$\displaystyle \int_{-\infty}^{-1} \frac{1}{\sqrt{2-w}}dw$
    work:$\displaystyle \lim_{t\to-\infty}\int_t^{-1}\frac{1}{\sqrt{2-w}} \, dw$ I used u substitution with $\displaystyle u=2-w$ leaving me with $\displaystyle \lim_{t\to-\infty}2\sqrt{2-w}$ from -1 to t
    answer: diverges. Sorry, delete this post
    Last edited by mr fantastic; Jul 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:$\displaystyle \int_{-\infty}^{-1} \frac{1}{\sqrt{2-w}}dw$
    $\displaystyle \int \frac{1}{\sqrt{2-w}}dw = -2 \sqrt{2-w}$

    So evaluated as a definite integral between $\displaystyle - \infty$ and $\displaystyle -1$ the integral does not converge.
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  3. #3
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    Quote Originally Posted by superdude View Post
    question:$\displaystyle \int_{-\infty}^{-1} \frac{1}{\sqrt{2-w}}dw$
    work:$\displaystyle \lim_{t\to-\infty}\int_t^{-1}\frac{1}{\sqrt{2-w}} \, dw$ I used u substitution with $\displaystyle u=2-w$ leaving me with $\displaystyle \lim_{t\to-\infty}2\sqrt{2-w}$ 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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