(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Integral from negative infinity to positive infinity of (1/(sqrt(1+x^2))dx

2. The attempt at a solution

Using trig substitution I got the integral equal to ln|sqrt(1+x^2) + x| Finding this was not the difficult part. Evaluating it is.

I set it up like this: lim b --> infinity and lim a --> neg infinity [(ln(sqrt(1+b^2)) + b) - (ln(sqrt(1+a^2)) + a)]

the 'b portion' goes to infinity. For the 'a portion' I rewrote it as ln|1/sqrt(1+x^2) - a| Plug in negative infinity and it is ln|1/infinity|. This is where im not sure what it is. If 1/infinity = 0, then isnt it indeterminate because you cannot take the ln(0)? If it is simply the ln(extremely small number) then it would be negative infinity, which means the overall answer is infinity, correct?

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# Improper Integral

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