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December 23rd, 2012, 07:44 AM   #1
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Improper integral

So i calculate this improper integral, given as an attachment. The final solution should be ln(2).

But the last step says: - ln(R) + ln(2) + ln(R-1) - ln(1)
If you replace R by ? you should get: - ln(?) + ln(2) + ln(? -1) - 0)

So i do not understand why - ln(?) and ln(? - 1) can be set equal to 0 so the final solution is ln(2)?
I thought ln(?) = ? ?
Attached Images
 improper.png (14.0 KB, 75 views)

 December 23rd, 2012, 07:51 AM #2 Math Team     Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions Re: Improper integral $\text{You can rewrite as : } \lim_{R \to \infty }\,\ln $$\frac{R-1}{R}$$$ $\ln $$\lim_{R \to \infty } \frac{R-1}{R}$$=\ln (1) =0$

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