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Math Help - integral with sqrt

  1. #1
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    integral with sqrt

    in the picture you can see the problem, i did a little bit of the way to solve it but i stuck now.

    hope you can help

    thanks.
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  2. #2
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    by the way 1 of the answer is between A-F.

    thanks.
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  3. #3
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    For \displaystyle \int_{\sqrt{2}}^{\sqrt{6}}\frac{1}{\left(\frac{x}{  \sqrt{2}}\right)^2+1}\;{dx}, let y = \frac{x}{\sqrt{2}}, then use:

    \displaystyle \int\frac{1}{y^2+1}\;{dy} = \arctan{y}+k.
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  4. #4
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    Another way to do it if you can't remember the formulas is through trig substitution. Draw a right triangle such that \displaystyle \tan( \theta) = \left( \frac{x}{\sqrt{2}} \right). Find d \theta in terms of x then substitute everything. You'll be left with a nice cancellation and an easy integral. Then back substitute. You'll get the same answer that TheCoffeeMachine is leading you to.
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  5. #5
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    hi thanks to both of you, so after i Calculate i find the answer is E .

    can you Please just tell me if i correct?

    thanks.
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  6. #6
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    Quote Originally Posted by ZOOZ View Post
    So after i Calculate i find the answer is E.
    Correct!
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