Integral from 0 to 1 of 1/sqrt(1+x^2)

  • Thread starter uman
  • Start date
  • #1
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Homework Statement


[tex]\int_0^1 \frac{1}{\sqrt{x^2+1}}\,dx[/tex]


Homework Equations


Integration by substitution looks like it might help here...


The Attempt at a Solution


The answer is [tex]\log (1+\sqrt 2)[/tex], but I'm at a loss as to how to derive that.
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
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You could try a trig substitution such as [itex]x=tan\theta[/itex].Hyperbolic trig sub. would be possible as well.
 
  • #3
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Thanks. I worked it out using your suggestion, but x = sinh(theta) also works, in case anyone cares. :-)
 

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