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Math Help - Integration by subtitution

  1. #1
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    Integration by subtitution

    Use the substitution x=tan\theta to find the exact value of

     <br />
\int{\frac{1-x^2}{1+x^2}}dx
    limits root 3 and 1

    I know, that when you sub you have to change the limits:
    root 3=tan\theta
    \theta=\frac{pi}{4}

    1=tan\theta
    \theta=\frac{pi}{4}

    Please show me how to do this.
    Thanks
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  2. #2
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     <br />
\int{\frac{1-x^2}{1+x^2}}dx
    limits root 3 and 1

    Please show me how to do this.
    Thanks[/quote]
    x = tanθ
    Then dx = sec^2(θ)*d(θ)
    When x = 1, θ = Π/4
    When x = sqrt(3), θ = π/3
    The given integration becomes
    int[(1-tan^2θ)/(1+tan^2θ)*sec^2(θ)*d(θ)
    That reduces to
    int[(1-tan^2(θ)*d(θ) between π/4 to π/3.
    Put tan^2(θ) = sec^2(θ) - 1 and solve the integration.
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  3. #3
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    Thats really helpful so far, but i can't remember how to integrate that. any hel there?
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  4. #4
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    What is the integration of sec^2(x)?
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  5. #5
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    oh yh, im being silly.
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