[SOLVED] improper integral

**superdude** · July 22nd 2009, 08:55 PM

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

**pomp** · July 22nd 2009, 09:02 PM

Originally Posted by superdude

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.

**mr fantastic** · July 22nd 2009, 11:51 PM

Originally Posted by superdude

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

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