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Integral problem

  1. Sep 13, 2008 #1
    1. The problem statement, all variables and given/known data
    [tex]Evaluate $\displaystyle\int^{1}_{0}{\sqrt{x^2+1}}$[/tex]

    2. Relevant equations

    3. The attempt at a solution
    [tex]By trigonometric substitution: $x = \tan{\theta} \rightarrow dx = \sec^2{\theta}\,d\theta$
    \[\int^{\frac{\pi}{4}}_{0}{\sec^2{x}\sqrt{\tan^2{\theta}+1}}\,d\theta = \int^{\frac{\pi}{4}}_{0}{\sec^3{\theta}}\,d\theta\]
    \[= \int^{\frac{\pi}{4}}_{0}{\sec{\theta}\tan^2{\theta}+\sec{\theta}}\,d\theta\][/tex]

    This is where I get stuck
  2. jcsd
  3. Sep 13, 2008 #2


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    Science Advisor
    Homework Helper

    Hi imranq! :smile:

    (have a theta: θ and a squared: ² and a cubed: ³ :smile:)

    Hint: (d/dθ)(secθ tanθ) = … ? :wink:
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