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Math Help - really stuck on this integral

  1. #1
    Member i_zz_y_ill's Avatar
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    really stuck on this integral

    use a trigonometric substitution to find integral of 1/(1+3x^2)^3/2 between limits 0 and 1.

    I think you have to use tan or sin not quite sure how though.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by i_zz_y_ill View Post
    use a trigonometric substitution to find integral of 1/(1+3x^2)^3/2 between limits 0 and 1.

    I think you have to use tan or sin not quite sure how though.
    let \sqrt 3x = \tan \theta

    now continue with the substitution process


    we use tan because we are using the 1 + \tan^2 (x) = \sec^2 x

    know your trig identities
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  3. #3
    Member i_zz_y_ill's Avatar
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    how does that work,

    thanks but cant see how that works. No doubt ur wright but I still can't do it..
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  4. #4
    Eater of Worlds
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    You can leave x=\frac{1}{\sqrt{3}}tan({\theta}), \;\ dx=\frac{1}{\sqrt{3}}sec^{2}{\theta}d{\theta}

    This changes your limits of integration to 0 to Pi/3.

    Making the subs will whittle it down to:

    \frac{1}{\sqrt{3}}\int_{0}^{\frac{\pi}{3}}{cos{\th  eta}}d{\theta}
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